力学学报

PROGRESS IN MOLECULAR DYNAMICS SIMULATIONS OF SURFACTANT SOLUTION FOR TURBULENT DRAG REDUCTION

Wei Jinjia, Liu Fei, Liu Dongjie

Surfactant additives for turbulent drag reduction have been widely used in energy power and chemical industry. The addition of a small amount of surfactant additives in the pipeline fluid can greatly reduce the flow friction resistance and save energy. In recent years, the research on the mechanism of surfactant drag reduction is also a hot scientific topic. This paper not only summarized our work on the rheology of surfactant solution, surfactant drag reduction, the correlation with surfactant drag reduction and heat transfer, Brownian dynamics simulations in the latest years, but also concerning some works based on the coarse grained molecular dynamics (CGMD) simulations in the past three years, which will be elaborated in detail. The CGMD simulation is developed these years and now widely used in chemistry, biology and many other aspects. Our CGMD simulation work includes three parts, which are the rheology properties and its microstructures of the surfactant solution, the mechanism of turbulent drag reduction by surfactant additives, the analysis of turbulent drag reduction failure phenomenon on the pipeline transportation system. Through reviewing the progress in our CGMD simulation work, we believe that the CGMD simulation method can reasonably explain the rheological behavior of surfactant solutions, and the relationship between the rheology and the surfactant micelle structure can be well studied by using the coarse grained model. The breakage and the recombination behaviors of surfactant micelles can be evaluated from a multidimensional system including the extensional energy, the breakage energy, the maximum reasonable stretching distance, coalescence energy, zeta potential, or hydrophobic driving effect. Besides, the "viscoelasticity theory" can be proved from a molecular scale. Last but not least, the mechanism of turbulent drag reduction failure phenomenon can also be analyzed by CGMD simulation by simulating different failure reasons. At last, we summarize the CGMD simulation work on surfactant in recent years and then the direction of the future work about CGMD simulation work on surfactant is predicted.

2019, 51(4): 971-990. doi: 10.6052/0459-1879-18-372

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OSCULATING-CONE WAVERIDER DESIGN BY CUSTOMIZING THE PLANFORM SHAPE OF LEADING EDGE

Liu Chuanzhen, Bai Peng, Wang Jifei, Liu Qiang

The waverider has been the current research focus because of high lift to drag ratio in hypersonic state, while some deficiencies of waverider limit its practical application in engineering. Osculating-cone method is one of the most widely applicable waverider design methods for engineering, yielding much flexibility and efficiency. In order to remedy some of the deficiencies and improve the flexibility for waverider, the article extends the application of the osculating-cone waverider design method, conducting the geometric relationships among the inlet capture curve, flow capture tube and planform contour line, expressed by a differential equation set. The equation set lays a solid foundation for the planform-controllable waverider design. By introducing the numerical solving strategy for the differential equation set, combining with some solving tips, the osculating-cone waverider design by customizing the planform shape of leading edge is proposed. Three validation cases are generated in the article including the gradually varied leading edge, "S" leading edge and double swept planforms from the osculating-cone waverider by customizing the planfrom shape of the leading edge. Using computational fluid dynamics method, the flow fields of these three configurations are calculated and analyzed. Results suggested that the hypersonic wave-riding performance maintenances for the waverider since the shock wave obtained from CFD matches well with the design curve and high lift to drag ratio is remained as traditional waverider. The method and the CFD results indicate that it permit us to customize the planform of waverider conveniently and efficiently. The geometric relationships expressed by a differential equation set provide a novel idea to improve the flexibility and remedy some of the deficiencies of waverider.

2019, 51(4): 991-997. doi: 10.6052/0459-1879-18-368

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NUMERICAL SIMULATION OF CYLINDRICAL CONVERGING SHOCK INDUCED RICHTMYER-MESHKOV INSTABILITY WITH SPH

Xu Jianyu, Huang Shenghong

The Richtmyer-Meshkov (RM) instability induced by converging shock waves at interfaces of different substances has an important academic significance and engineering background in the field of inertial confinement fusion. The macroscopic fluid dynamics method based on grid discretization requires high order precision algorithm to track the interface evolution accurately because of numerical diffusion problem, and it is extremely difficult to track the complex interface evolution such as large deformation and fragmentation merging, etc. Smoothed particle hydrodynamics (SPH) method is a pure Lagrangian algorithm, which can effectively overcome the addressed difficulties. However, the classical SPH algorithm requires artificial viscosity to smooth the strong discontinuities, otherwise large non-physical oscillations may occur. For the problem involving strong shock instability, it is difficult to achieve ideal results. In this paper, the SPH algorithm based on HLL Riemann solver is adopted to effectively distinguish and track the strong shock wave and the material interface with a large density ratio. The reliability and robustness of the code were validated by four classical 1D shock tube tests, and it is found that the smoothing effect of the density algorithm used by SPH on the contact discontinuity can be improved by reducing the initial particle spacing. The smaller the initial particle spacing, the higher the numerical simulation accuracy, but it cannot be completely eliminated. However, the position of the interface is actually marked by the media properties of the particles, and does not affect the discrimination of the interface position under the SPH Lagrangian algorithm. Then the 2D cases of RM instability induced by cylindrical converging shock wave impacting at the quadrilateral light/heavy gas interface were simulated. It is found that the simulation results are quantitatively in good agreement with the existing experimental results. By analyzing the density and pressure changes in the process of interface evolution, it is also found that the models and methods adopted can accurately track the complex interfaces and shock waves evolution patterns during the RM instability process. The relevant results lay a foundation for further understanding and explanation of RM instability mechanism under extreme converging shock conditions.

2019, 51(4): 998-1011. doi: 10.6052/0459-1879-19-041

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EFFECTS OF THERMOCHEMICAL AND TRANSPORT MODELS ON THE HIGH-SPEED DOUBLE-CONE FLOWFIELD

Cong Binbin, Wan Tian

The shock wave and boundary layer interaction is common during hypersonic flight, and it is critical for the aerodynamic performance and safety of the flight vehicle. When the enthalpy of the incoming flow is high, its numerical simulation is challenging due to many complex physics and chemistry phenomena whose modelling requires further investigation and study. Hypersonic flow around a double-cone is selected as the test case and the effects of thermochemistry and transport models on the wall pressure and heat transfer rate are studied numerically. The thermochemical models include perfect gas model, thermal non-equilibrium with frozen or non-equilibrium chemistry, and thermal equilibrium with non-equilibrium chemistry. The transport models include the widely used Wilke/Blottner/Eucken model, and the more physically complicated Gupta/SCEBD model. Moreover, the influence of wall catalysis is also considered. The six experimental test runs, covering from low to high enthalpy inflow conditions, are simulated. The computed results show that the computed wall pressure and heat flux agree with the experiments. Under the low enthalpy condition, the distribution of the molecular internal energy has a big impact on the results, and the two transport models produce similar results. Under the high enthalpy condition, the chemical reaction and wall catalysis have a significant influence. Comparison of the results with the different transport models shows much larger difference for higher freestream enthalpy.

2019, 51(4): 1012-1021. doi: 10.6052/0459-1879-19-022

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PROPAGATION CHARACTERISTICS OF CURVATURE WAVE ALONG THE BODY IN ANGUILLIFORM FISH SWIMMING

Shen Haoyan, Zhu Bowen, Wang Zhihui, Yu Yongliang

In this study, the homogeneous viscoelastic beam with a variable cross-section is used to model the lamprey, an anguilliform (eel-like) swimmer, and to research the propagation characteristics of the curvature wave driven by an active bending moment wave along the fish body. The results show that as long as the excitation frequency is higher than the structure fundamental frequency of the fish body, there will be a phase lag between the two waves, which increases from the head to the tail of the fish body. The increasing phase lag indicates that there exists a speed difference between propagations of the active bending moment and the body curvature, that is, the speed of the later is lower than that of the former. This features are consistent with the experimental results published. The dimensional analysis indicates the ratio of the speed of bending curvature wave to that of the active bending moment wave is associated with the dimensionless excitation frequency, wavelength and damping coefficient, but independent of the swimming Reynolds number. For anguilliform (eel-like) swimmers, the wave speed ratio decreases with increasing frequency or wave length of active bending moment, and it rises if the damping coefficient becomes larger. In addition, we also carried out a small perturbation analysis to linearize the equations, and found an integrated similarity parameter which includes the dimensionless frequency, wave length and damping coefficient. This parameter can uniformly describe the dependence of the speed ratio on the excitation and material parameters.

2019, 51(4): 1022-1030. doi: 10.6052/0459-1879-19-087

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STUDY OF PROCESS CONTROL ON PIEZOELECTRIC DROP-ON-DEMAND EJECTION

Liu Zhaomiao, Xu Yu, i, Pang Yan, Ren Yanlin, Gao Shanshan

The size and uniformity of micro-droplets are key factors influencing the quality of the molded part by micro-droplet ejecting additive manufacturing technology. In this paper, a piezo-actuated micro-droplet ejection device for generating uniform micro-droplets is studied. The piezoelectric material drives the flexible diaphragm to vibrate and pushes the liquid out of the nozzle and produces micro-droplets. The amplitude of the diaphragm under different control parameters and its influence on the size and uniformity of the generated micro-droplets are investigated by numerical simulation and experiment. The results indicate that the amplitude of the diaphragm is affected by the driving voltage and the piezoelectric frequency and the experimental value of the diaphragm's center point amplitude is less than that of the theoretical calculation value which is mainly influenced by the piezoelectric frequency. The amplitude of the diaphragm will change the pressure inside the nozzle, which leads to the varied sizes of the micro-droplet. When the driving voltage is constant, the diaphragm has the maximum amplitude for the piezoelectric frequency at 10 Hz. As the amplitude of the diaphragm increases, droplets can be generated when the liquid velocity at the orifice and the length of the liquid column increase to a critical value. As the amplitude of the diaphragm continues to increase and the length of the liquid column at the orifice is beyond to a critical value, a satellite micro-droplet is formed. When the amplitude range of the membrane is between 30 $\mu $m and 42 $\mu $m, micro-droplets can be stably formed whose uniformity and size meet the demand well, and the minimum generating micro-droplets size is 339.8 $\mu $m. The maximum change rate of droplet diameter and adjacent two droplets are 0.29% and 2.67% respectively. Results are benefit to promote the uniformity of micro-droplets and will provide a reference for the development of piezoelectric droplet ejection devices.

2019, 51(4): 1031-1042. doi: 10.6052/0459-1879-19-035

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HIGH-FIDELITY SIMULATION OF WAVE PROPAGATION BASED ON VPM-THINC/QQ MODEL

Nie Longfeng, Zhao Xizeng, Zhang Zhihang, Tong Chenyi, Wang Chen

In order to achieve high-fidelity of numerical simulation of wave propagation, an improved finite volume method with volume-average and point-value (VPM) is used to solve the Navier-Stokes equation and the tangent of hyperbola for interface capturing with quadratic surface representation and Gaussian quadrature reconstructs the free surface. The VPM-THINC/QQ model based on OpenFOAM underlying function library is established. The piston wave-making method is added to the current model to realize the wave generation, and the relaxation method is used to realize the wave dissipation. A high-precision viscous numerical wave water tank is built. The numerical simulation of regular waves is carried out by using VPM-THINC/QQ model and interFoam solver (multiphase solver widely used in OpenFOAM software packages) respectively. The effects of grid size and time step on the wave propagation process are investigated mainly. The attenuation degree of wave height is quantitatively compared and analyzed. In order to verify the adaptability of the current model, simulation of long and short waves is carried out. The results show that under the same grid size or time step, the prediction results of the VPM-THINC/QQ model agree well with the theoretical solution compared with the interFoam solver. The wave height has little attenuation and there is no phase difference. It shows high-fidelity of the VPM-THINC/QQ model in the wave propagation process. A high-precision model of viscous numerical wave tank is provided for studying the wave propagation process in this work.

2019, 51(4): 1043-1053. doi: 10.6052/0459-1879-18-454

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CHEMOMECHANICAL ANALYSIS OF A FUNCTIONALLY GRADED SPHERICAL HYDROGEL

Yang Jianpeng, Wang Huiming

As a kind of new smart materials, hydrogel has a special chemomechanical coupling effect. By using the functionally graded material, the adaptability and controllability of the hydrogel can be improved distinctly. In this analysis, the crosslink density of the hydrogel is assumed to be a power-law function of the radial position. By employing the general multi-field coupling large deformation theory and the Flory-Huggins free energy function, the governing equations of the functionally graded spherical hydrogel (FGSH) undergoing the spherically symmetric deformation are developed. The theoretical analysis of the swelling behavior accompanying the inhomogeneous large deformation is presented for the FGSH when subjected to the internal pressure and the prescribed chemical potential. Numerical results show that both the internal pressure-internal radius curve and the internal pressure-radial stretch curve exhibit a stable region and an unstable region, which means that if the internal pressure exceeds a certain critical value, the instability will occur and the hydrogel will finally be damaged. The critical value of the internal pressure increases with the increasing of gradient index. It is shown that the material parameters, such as gradient index, the interaction parameter between the polymer network and the solvent, the cross-link density and the volume of the solvent molecular, and the environmental chemical potential have a significant effect on the swelling behavior of the FGSH. If the internal pressure is fixed, the radial displacement of FGSH at the internal surface is nearly linear with respect to the gradient index, while it appears obvious nonlinear to other parameters. The investigation is helpful to realize the precise control of the hydrogel-based smart structures and devices under the complex environments.

2019, 51(4): 1054-1063. doi: 10.6052/0459-1879-19-019

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FULL FIELD DIC ANALYSIS OF ONE-DIMENSIONAL SPALL STRENGTH FOR CONCRETE

Yu Xinlu, Fu Yingqian, Dong Xinlong, Zhou Fenghua, Ning Jianguo, Xu Jipeng

The one-dimensional stress spalling experiment of concrete bar was carried out based on a $\varPhi $74 mm SHPB experimental platform. The displacement and velocity field on the surface of concrete bar were measured by using digital image correlation method (DIC), which can digitalize and calculate the photos of movement of specimen recorded by an ultra-high speed video camera with the high-resolution sampling rate of 2 $\mu $s/frame. The strain field also can be achieved by DIC method. The analyzed results of displacement and strain fields show that multiple spalling occurs in a sequence of time near the far end of the concrete bar. It has been confirmed that the concrete bar stays in the one-dimensional stress state when the fracture occurs for that the tensile stress of each position is superimposed by the transmission compression wave and the reflection tensile wave, so that the one-dimensional stress wave propagation analysis can be applied. We put forward a criterion for judging the occurring moment of the spall according to the change of the velocity trend of the two point across the crack position. The criterion can give the starting time of all the spall cracks, and for each spalling crack the tensile failure strain, failure strength, and the strain rate is determined directly. The results show that the tensile strength of the concrete bar exhibits a strong strain rate dependency, with the dynamic increase factor (DIF) reaching 5 as the strain rate is 30 s$^{-1}$. Compared with the traditional methods (wave superposition method, pull-back method), the DIC full-field analysis method, which is not limited by the loading waveform, can give the exact starting time of each crack position. Therefore, it is possible to analyze the fracture strain and strain rate of the specimen at different positions, where have different strain rates, under higher strain rate loading.

2019, 51(4): 1064-1072. doi: 10.6052/0459-1879-19-008

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TOPOLOGY OPTIMIZATION OF PIEZOELECTRIC ACTUATOR CONSIDERING CONTROLLABILITY

Hu Jun, Kang Zhan

Piezoelectric actuators can convert electrical energy into mechanical energy, and has application potential in active vibration control of structures. Since the layout of the piezoelectric actuators has a great influence on the vibration control effect, the optimization of the actuators has always been one of the key factors to structural control. In order to improve the efficiency of control energy in the piezoelectric structure, this paper proposes a topology optimization method for the layout design of piezoelectric actuators with the goal of improving structural controllability. The finite element modeling of the piezoelectric structure is carried out based on the classical laminate theory. The modal superposition method is used to map the dynamic governing equation to the modal space. The controllability index based on the singular value of the control matrix is derived. In the optimization model, the exponential form of the controllability index is chosen as the objective function, and the design variables are the relative densities of the actuator elements. Based on the Solid Isotropic Material Penalization method, an artificial piezoelectric coefficient penalty model is constructed. Sensitivity analysis for the controllability index is proposed based on the singular value of the control matrix. The optimization problem is solved by a gradient-based mathematical programming method. Numerical examples verify the effectiveness of the sensitivity analysis method and the optimization model and show the significance of the layout design of piezoelectric actuators. The influence of some key factors on the optimization results are discussed. It shows that the more piezoelectric materials, the better the controllability; the modes of interest in the objective function has a great influence on the layout of the piezoelectric actuators.

2019, 51(4): 1073-1081. doi: 10.6052/0459-1879-19-012

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NUMERICAL SIMULATIONS OF TAYLOR IMPACT EXPERIMENTS OF QUARTZ GLASS BARS

Xiong Xun, Wang Zhu, Zheng Yuxuan, Zhou Fenghua, Xu Zhen

The Taylor impact experiments of quartz glass bar were simulated by using a discrete element method (DEM) approach. The simulations provided detailed failure process of the glass bar: at the impact end, the bar failed in the form of compressive failure wave; at the free end, dense tensile spallation failure occurs. The analysis showed that the spallation is the result of the interaction between the chasing unloading waves caused by the rapid decrease of stress in the failure wave front, and the incoming unloading wave caused by the reflection of the elastic compression wave front at the free end. With the impact velocity increasing, the size of the compressive failure zone increases at the impact end, and the spallation failure zone decreases at the free end. Furthermore, the structural fronts and their propagation velocity of the compressive failure zone were investigated. It was found that the "failure front" in fact was a transition zone from dense crack region (the high damage region, HDZ) to sparse crack region (the low damage zone, LDZ). It was found that the propagation velocity LDZ front is basically the same as the elastic wave velocity, which is a constant. However, the HDZ front velocity decreases as it propagates. The average velocity of the HDZ front increases with the increasing of the impact velocity, and may approach the limit value of elastic wave velocity. In experiments, people usually reports the high-speed video observations of "failure waves" in glass bar after impact, which are actually the front of the HDZ, as the dense cracks formed the HDZ reflect lights to make the region bright and observable.

2019, 51(4): 1082-1090. doi: 10.6052/0459-1879-19-017

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IDENTIFICATION OF MULTIPLE FLAWS IN STRUCTURES BASED ON FREQUENCY AND MODAL ASSURANCE CRITERIA

Jiang Shouyan, Zhao Linxin, Du Chengbin

Static response (displacement, strain, etc.) can hardly be recorded by a group of sensors installed on the structure in the inversion analysis of practical problems, while the dynamic characteristics (frequency, mode) and dynamic response (acceleration, velocity, dynamic displacement) of the structure can be easily acquired by sensors in practical problems. In this paper, the objective function of the inversion analysis model is constructed based on frequency residuals and modal assurance criteria. Combining the advantages of dynamic extended finite element method in frequency domain and artificial bee colony intelligent optimization algorithm, the extended finite element method avoids re-meshing in each iteration by introducing discontinuous displacement approximation and can reflect the number, location and size of defects by changing the level set function. In each iteration, the artificial bee colony intelligent optimization algorithm uses global and local searches. The probability of finding the optimal solution increases greatly and avoids local optimum. At the same time, by introducing topological variables, the number of flaws is incorporated into the inversion analysis process. The number of flaws can be intelligently inverted in the iteration process. Then, the inversion analysis model of multiple flaws (voids, cracks) in the structure is established. The analysis of several examples shows that the inversion analysis model can accurately detect the number, location and size of circular flaws, elliptical flaws, or crack in the structure. The result also shows the good robustness of the algorithm.

2019, 51(4): 1091-1100. doi: 10.6052/0459-1879-19-078

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APPLICATION OF DISCONTINUOUS DIGITAL IMAGE CORRELATION IN CRACK RECONSTRUCTION

Tang Wenzhi, Xiao Hanbin, Zou Sheng

The digital image correlation (DIC) method is a new non-destructive, contactless displacement measurement approach and it can be broadly applied in mechanical engineering with wide application prospect. However, this efficient and convenient displacement measurement method is difficult to apply in fracture mechanics due to the limitation that continuous deformation is required when processing the deformed images with standard digital image correlation methods. Aiming at solving this problem, this paper proposes a novel discontinuous digital image correlation (DDIC) method by introducing the splitted subset model to take the place of continuous model and use it to analyze the discontinuous areas where standard digital image correlation method is not valid in. The displacement of the original pixel points is studied when discontinuities such as cracks occurs, and the crack opening vector is introduced to represent the displacement relationship between the master zone and the slave zone after subset splitting into two parts. Thus the mathematical model of the splitted subset can be established by using the crack opening vector to correlate the master zone and the slave zone, and the corresponding image correlation algorithm can be designed based on this model. Afterwards, the proposed discontinuous digital image correlation method is used to measure the displacements of the deformed images obtained from the cracking process when a tensile test is applied to the notched plate. The research results show that the proposed DDIC method works well in both continuous and discontinuous areas, and when compared with the standard DIC method, the DDIC method is capable to solve the validation problem of image correlation method in discontinuous region, and improves the accuracy for displacement measurement, moreover, the proposed method is able to reconstruct the crack faces and the displacement fields in the vicinity region crack, and the accuracy of displacement measurement can be controlled within the range of subpixel level.

2019, 51(4): 1101-1109. doi: 10.6052/0459-1879-19-098

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NONLINEAR DYNAMICAL CHARACTERISTICS OF A MULTI-STABLE SERIES ORIGAMI STRUCTURE

Qiu Hai, Fang Hongbin, Xu Jian

Recently, origami structures and origami mechanical metamaterials receive extensive attention from the science and engineering communities due to the infinite design space, excellent deformability, extraordinary mechanical properties, and wide application potentials. In particular, some origami structures have been well studied due to their unique bistability. Note that origami structures and origami metamaterials are always composed of multiple cells; however, for multi-cell origami structures, their multistability characteristics and the induced dynamical behaviors have not been well understood. On the basis of the bistable stacked Miura-ori structure, this paper studies an origami structure connected by two heterogeneous cells in series based on force balance. Static analysis suggests that the two-cell series structure have four different stable configurations, exhibiting a multi-stable profile. Dynamical analysis reveals that the two-cell series origami structure presents significantly different natural frequencies at the four stable configurations. With the increase of the excitation amplitude, the multistability of the two-cell series structure could induce complex nonlinear dynamical responses, including intrawell and interwell oscillations that are sub-harmonic, super-harmonic, or even chaotic. They can be classified into nine types based on the response amplitude characteristics. Moreover, the basin of attraction and the basin stability of these dynamical responses are examined. The results indicate that the basin stabilities (i.e., the appearing probabilities) of these types of dynamical response are significantly different and closely relate to the excitation amplitude. In summary, the outcomes of this paper, i.e., the static characteristics of the two-cell series structure, the classification on dynamical responses, and the evolution rule of the basin stabilities with respect to the excitation amplitude, would contribute to the understanding on the nonlinear dynamics of multi-stable origami structures, and provide the basis for controlling the nonlinear dynamical responses.

2019, 51(4): 1110-1121. doi: 10.6052/0459-1879-19-115

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THE COMPLEX DYNAMICS OF ABNORMAL PHENOMENON OF NEURAL ELECTRONIC OSCILLATIONS INDUCED BY NEGATIVE FEEDBACK

Lan Yuqun, Guan Linan, Gu Huaguang

In traditional viewpoint, it is easy to achieve stable equilibrium for a system with negative feedback and stable oscillations for a system with positive feedback. In the present investigation of the nonlinear neural system, a novel viewpoint that negative feedback can induce stable equilibrium, i.e. the resting state, changed to oscillations, i.e. firing, is proposed. In a theoretical neuron model, inhibitory stimulation mediated by the negative impulsive current with enough strength can induce an action potential from the resting state near a Hopf bifurcation point and the after-potential with damping oscillations following the action potential. The strength threshold of the second negative impulsive current applied within the after-potential to evoke the second action potential exhibits damping oscillations as well with respect to the application phase of the current. After introducing negative feedback with time delay ($\tau $) into the theoretical model to simulate the inhibitory autapse, the negative feedback current induced by an action potential is applied at the phase $\tau $ of the after-potential following the action potential. The negative feedback gain threshold to induce firing from the resting state exhibits characteristics of damping oscillations with increasing time delay corresponding to application phase of the current, which resembles the time delay induced-multiple coherence resonances. The oscillation period is associated with the period of strength threshold curve of the second impulsive current to evoke the second action potential from after-potential and the period of the firing near the Hopf bifurcation. Furthermore, the negative feedback can also induce complex dynamics such as the coexistence of the firing and resting state. The results of the present paper not only present a novel modulation effect of the negative feedback, which is a contrast to the tradition viewpoint, but also are helpful for understanding the potential functions of slow inhibitory autapse that can induce negative impulsive current with time delay in the real neural system.

2019, 51(4): 1122-1133. doi: 10.6052/0459-1879-19-038

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DYNAMIC CHARACTERISTICS ANALYSIS OF A ROTATING FLEXIBLE CURVED BEAM WITH A CONCENTRATED MASS

Wu Ji, Zhang Dingguo, Li Liang, Chen Yuanzhao, Qian Zhenjie

The dynamic characteristics of a planar rotating flexible curved beam with a concentrated mass are studied in this paper. The curved beam element is derived based on the absolute nodal coordinate formulation. The element adopts the Green-Lagrangian strain, and the virtual work of the elastic force of the curved beam element is calculated according to the curvature change before and after the deformation of the curved beam and the exact expression of the curvature. Through the virtual work principle, the nonlinear dynamic model of rotating flexible curved beam with a concentrated mass is established by using the $\delta $ function and the fixed boundary condition between the hub and the cantilever curved beam. Based on this model, the pure bending problem of cantilever curved beam and the dynamic response of rotating flexible curved beam with rigid-flexible coupling effect are simulated. According to the results, the convergence of the proposed element and the correctness of the dynamic model are discussed, respectively. Furthermore, applying the D'Alembert principle, the rotating curved beam is equivalent to a non-rotating curved beam with centrifugal forces, and the characteristic equations of the system are obtained by linear perturbation processing. The effects of rotating angular velocity, initial curvature and concentrated mass on the dynamic characteristics of the curved beam are studied, respectively. Finally, the frequency loci veering and mode shift of the rotating curved beam are analyzed, and the interrelation between them is expounded. The results show that with the increase of rotation angular velocity, the frequency characteristics of curved beams are similar to straight beams, and the mode shapes of curved beams dominated by tensile deformation will be advanced.

2019, 51(4): 1134-1147. doi: 10.6052/0459-1879-19-027

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ENERGY HARVESTING ANALYSIS OF A PIEZOELECTRIC CANTILEVER BEAM WITH MAGNETS FOR FLOW-INDUCED VIBRATION

Cao Dongxing, Ma Hongbo, Zhang Wei

Flow-induced vibration contains tremendous energy. Based on the theory of flow-induced vibration, a kind of flow-induced vibration energy harvester with additional magnetic excitation is designed, and its vibration energy harvesting characteristics are studied theoretically and experimentally. The harvester consists of a piezoelectric cantilever beam, a circular cylinder and magnets. Firstly, based on the Euler-Bernoulli beam theory, the energy functions of the magneto-piezoelectric energy harvester with fluid-induced vibration excitation are derived, and the electromechanical coupling equation is established by using the Hamilton principle. Then, the influence of the system parameters such as the flow velocity, the diameter and length of the circular cylinder, the magnetic parameters and the external resistance on the vibration characteristics and output voltage of the piezoelectric energy harvester. The results show that the vibration amplitude of the piezoelectric harvester produces vortex-induced vibration at low flow velocity and output the maximum voltage; the magnetic force can reduce the resonance frequency of the structure and broaden the bandwidth harvester. Thus, the magnetized piezoelectric harvester is more suitable for low-speed flow environment than the non-magnetized piezoelectric harvester. The experimental results agree well with the numerical results, which verifies the results of the theoretical analysis of the magneto-piezoelectric energy harvester.

2019, 51(4): 1148-1155. doi: 10.6052/0459-1879-18-426

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MECHANICAL SIMULATION AND FULL ORDER SLIDING MODE COLLISION AVOIDANCE COMPLIANT CONTROL BASED ON NEURAL NETWORK OF DUAL-ARM SPACE ROBOT WITH COMPLIANT MECHANISM CAPTURING SATELLITE

Zhu An, Chen Li

The problem of collision avoidance compliance control for dual-arm space robot to protect joint due to impact in the process of capturing satellite is discussed. For this reason, a rotatory series elastic actuator (RSEA), a compliant mechanism, is designed between the joint motor and the manipulator. It has two functions: firstly, the impact energy of satellite to robot joints can be absorbed by RSEA's built-in spring through stretching or compressing in the capture operation; secondly, the impact torque of the joints can be limited in the safe range by reasonably designing a matching collision avoidance compliance control strategy. First of all, the dual-arm space robot with compliant mechanism open-loop subsystem dynamics model and the target satellite subsystem dynamics model are established before capture operation by the second Lagrange equation. Then, based on the momentum conservation and geometric constraints of the position and velocity of the closed-chain system, the closed-chain hybrid system of the space robot and the captured satellite is obtained after the capture operation. Finally, for calm control the hybrid system, based on RBF neural network, a full-order terminal sliding mode collision avoidance compliance control scheme is proposed. The proposed scheme not only can effectively absorb and buffer the impact energy in the capture operation, but can turn on or off the space robot's joint motor timely when the impact energy is too large, so as to avoid overload and damage of the joint actuator. In addition, the joint torques are allocated by the minimum weight norm theory to ensure the coordinated operation between manipulators. The global stability of the system is proved by the Lyapunov theory. At last, the effectiveness of the collision avoidance compliance control strategy is verified by computer simulation.

2019, 51(4): 1156-1169. doi: 10.6052/0459-1879-18-407

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CLOSED-FORM SOLUTIONS FOR FORCED VIBRATIONS OF CURVED PIEZOELECTRIC ENERGY HARVESTERS BY MEANS OF GREEN'S FUNCTIONS

He Yanli, Zhao Xiang

This article investigates the forced vibrations of curved piezoelectric energy harvesters by means of Green's functions. The differential method is used to analyze the in-plane forces of the cantilevered piezoelectric energy harvester. According to the governing equations of motion, the electromechanical coupled Prescott models are derived based on the piezoelectric constitutive relations, which the circumferential forcing and the circumferential inertia term can be negligible, and a damping effect, radial damping, is taken into account. Utilizing the Laplace transform, the explicit expressions of the Green's functions of the coupled vibration equations can be acquired. On the basis of the superposition principle and the physical interpretation of Green's functions, the coupled system is decoupled and the expression of the output voltage can be obtained analytically. The present model for the curved beam can be readily reduced to straight beam. In the numerical sections, the present solutions are verified by the results in some published references. By comparing with the result of traditional straight piezoelectric energy harvesters model, the high energy harvesting efficiency of the curved piezoelectric energy harvesters model in the thesis is demonstrated. It is apparent that the present model has a wider range of application than the existing ones. The influence of radial damping, Young's modules of two materials and some other essential physical parameters on the evaluation functions for output voltage and resonant frequency are discussed. This research suggests that to make the electric power reach the maximum value, the optimal resistive load is 1 M$\Omega$; the elasticity modulus for both piezoelectric material and structure material have a profound effect on the resonant frequency. By replacing the base materials with lower modulus of elasticity, the phenomenon of high frequency resonance can be improved to make the curved piezoelectric energy harvesters adapt to more complex working environment. However, the energy harvesting efficiency of the structure will be decline.

2019, 51(4): 1170-1179. doi: 10.6052/0459-1879-19-007

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BIFURCATION AND CHAOS OF AXIALLY MOVING BEAMS UNDER TIME-VARYING TENSION

Chen Ling, Tang Youqi

The transverse parametric vibration of the axially moving structure is always one of the hot topics in the field of nonlinear dynamics. At present, most of the studies are considering the time-varying speed of dynamic model. The parametric excitation comes from harmonic fluctuations of the axial speed. However, the fluctuation of the axial tension in an axially moving structure is more extensive in the engineering application. There are few researches considering the time-varying tension. The bifurcation and the chaotic behavior of axially accelerating viscoelastic beams under time-varying tension are studied in this paper. A nonlinear integropartia-differential governing equation of the moving beam is established. The linear viscous damping and the Kelvin model in the viscoelastic constitution relation are introduced. The axial tension is assumed as a harmonic variation with time. The fourth-order Galerkin truncation is employed to discretize the governing equation. The dynamic behavior of axially accelerating viscoelastic beams is determined by applying the fourth-order Runge-Kutta algorithm. The influences of material's viscoelastic coefficients, the mean axial speeds, the axial tension fluctuation amplitudes, and the axial tension fluctuation frequencies on the bifurcation diagrams are demonstrated by some numerical results of the displacement and velocity at the midpoint of the beam. The maximum Lyapunov exponent diagram of the system is used to identify the period motion and chaos motion. The results show that the smaller mean axial speed leads to the periodic motion. The period-doubling bifurcation and chaotic behavior are easy to occur near the critical speed. The larger axial tension fluctuation amplitude results in the larger chaos interval. The less viscoelastic coefficient and axial tension fluctuation frequencies lead to the chaotic behavior of the axially moving beam. Furthermore, chaos motions are confirmed using different factors, such as the time history, the fast Fourier transforms, the phase-plane portrait and the Poincaré map.

2019, 51(4): 1180-1188. doi: 10.6052/0459-1879-19-068

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EFFECT OF CONTACT NONLINEARITY ON ACOUSTIC BLACK HOLE BEAM FOR VIBRATION DAMPING

Li Haiqin, Kong Xianren, Liu Yuan

Acoustic black hole effect (ABH) refers to a passive vibration mitigation technique which takes advantage of flexural wave properties in thin structures with variable thickness. Focusing on the problem that the classical linear ABH is efficient only at high frequency range but less than desirable in the low frequency domain, this paper proposes the idea of using contact nonlinearity to transfer the energy from low to high frequency range, in order to improve the overall efficacy of the ABH. Considering the vibration of an ABH beam in contact with a rigid barrier from below it, an experimental study is firstly carried out to show the nonlinear phenomena and energy transfer induced by the contact nonlinearity. Then, a numerical model is derived from Euler-Bernoulli beam theory, with convergence properties studied. The model follows the general procedures of modal approach, while the eigenvalue problems are computed using a finite difference method due to thickness variation. The contact force is handled by Hertzian contact law, and the damping layer is dealt with a Ross-Kerwin-Ungard model. Detailed studies considering contact nonlinearity are thus conducted to precisely quantify the energy transfer and decay, and the gain in efficiency of the ABH, with parametric effect respect to the contact stiffness, initial gap and longitudinal location of contact points. It is demonstrated that when the contact nonlinearity is induced to the system, the vibrational energy can be transferred from the low frequency band-where the ABH is inefficient, to the high frequency range-where the ABH is effective, the energy decay in the beam is remarkably accelerated, and the overall performance of the ABH effect is significantly improved.

2019, 51(4): 1189-1201. doi: 10.6052/0459-1879-18-392

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ENERGY CODING OF HEMODYNAMIC PHENOMENA IN THE BRAIN

Peng Jun, Wang Rubin, Wang Yihong

The coding and decoding of neural information is the core research content in neuroscience, and it is also very challenging. The traditional neural coding theories have their own limitations, and they are difficult to provide effective theory from the global operation mode of the brain. Since energy is a scalar and has superposition, the theory of energy coding can study the global neural coding problem of the brain function from the prospective of energy characteristics of neuron activities, and has achieved a series of research results. Based on the Wang-Zhang neuron energy calculation model, this paper constructed a multi-level neural network, and we obtained the changes of the energy consumption of the neural network and energy supply of glucose in the blood by numerical simulation. The calculation results showed that the time of peak supply of glucose in the blood is delayed about 5.6 seconds compared to the time when the neural activity of the network reaches its peak, which reproduced hemodynamic phenomena in functional nuclear magnetic resonance (fMRI) from a quantitative perspective: after a five to seven seconds delay in the activation of a brain region, the change in cerebral blood flow increases dramatically. The simulation results showed that negative energy mechanism, which was previously reported by our group using Wang-Zhang neuronal model, played a central role in controlling the hemodynamics of the brain. Also, it predicted the neural coupling mechanism between the energy metabolism and blood flow changes in the brain under the condition of stimulation, which was determined by imbalance and mismatch between the positive and negative energy during the spike of neuronal action potentials. The research results in this paper provided a new research direction for further exploring the physiological mechanism of hemodynamic phenomena in the future, and gave a new perspective and research method in the modeling and calculation of neural networks.

2019, 51(4): 1202-1209. doi: 10.6052/0459-1879-19-010

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A NONLINEAR STRENGTH CRITERION AND TRANSFORMATION STRESS METHOD

Wan Zheng, Song Chenchen, Meng Da

The curve is expressed by a power parameter curve in the space of normal stress and shear stress. The outer tangent point of the curve and the mohr's circle corresponds to the point of failure stress point. Then, the inverse tangent value of the slope of the outer tangent line at the point is used to obtain the effective slip Angle.There are three effective slip angles for a three-dimensional element, and three effective slip angles are used to determine the effective slip surface of space. Based on the basic features of geotechnical materials as friction materials, the stress ratio on the effective slip surface is taken as a certain value to judge whether the material is damaged or not. The t strength criterion was derived based on the above ideas, in deviatoric plane, the shape of t criterion is a closed curve between Von-Mises criterion and SMP criterion. In the meridian plane, the introduction of open power function as a reflection of the curve of the effect of hydrostatic pressure and shear failure, and closed droplet type yield criterion function is adopted to reflect volume compression yield curve, reflect the compression-shear coupling characteristics of geotechnical material. Based on the proposed t strength criterion, the transformation stress formula is derived, which can easily transform the two-dimensional model by using $p$ and $q$ as the stress variables into a three-dimensional stress state constitutive model. Through the test and comparison of strength and various stress paths, the rationality of the proposed t criterion and the transformation stress formula based on the criterion is verified.

2019, 51(4): 1210-1222. doi: 10.6052/0459-1879-19-039

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NON-UNIFORM TIME STEP TVD SCHEME FOR PROBABILITY DENSITY EVOLUTION FUNCTION WITH IMPROVEMENT OF INITIAL CONDITION

Shi Sheng, Du Dongsheng, Wang Shuguang, Li Weiwei

Randomness appears widely in practical engineering problems, and nonlinear stochastic response analysis of complex structures is one of the major difficulties. Fortunately, the probability density evolution method proposed in recent years has provided a feasible way to solve this kind of problem. Due to the complexity of practical engineering problems, however, the probability density evolution function is commonly solved by time-consuming numerical methods. Hence, it is crucial to improve the computational efficiency and accuracy of these numerical algorithms. Base on the non-uniform mesh partitioning technique, a new kind of non-uniform time step TVD (total variation diminishing) scheme for probability density evolution function was derived, which improves the computational efficiency by reducing the number of iterations to 43.4%. With the increase of sample duration, the error of estimated mean value remained almost constant, while the error of estimated standard deviation increased accordingly, but the increase rate tended to diminish. The computing time also increased as the sample duration increased, but unusual cases appeared due to the adaptive time step mesh partitioning of the randomly generated samples. In addition, a new kind of initial condition with cosine function form is proposed based on the conventional initial condition with pulse-like function form. The result revealed that the initial condition with pulse-like function form is a special case of the proposed cosine function form initial condition, and the initial condition with cosine function form possesses better accuracy than the initial condition with pulse-like function form when a proper parameter is selected. The improved TVD scheme for probability density evolution equation on non-uniform time step grids with improved initial condition is illustrated with several numerical examples provided in the last section. The work accomplished in this paper is a supplement for the solving method of probability density evolution equation, and provides a basis for engineering application.

2019, 51(4): 1223-1234. doi: 10.6052/0459-1879-18-446

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ADAPTIVE BUBBLE METHOD USING FIXED MESH AND TOPOLOGICAL DERIVATIVE FOR STRUCTURAL TOPOLOGY OPTIMIZATION

Cai Shouyu, Zhang Weihong, Gao Tong, Zhao Jun

In this paper, an improved topology optimization approach named adaptive bubble method (ABM) is proposed to overcome the shortcomings of the traditional bubble method, such as the frequent remeshing operation and the tedious merge process of holes. The main characteristics of ABM are summarized as follows: (1) The finite cell method (FCM) is adopted to perform high-precision numerical analysis within the fixed Eulerian mesh, so that the processes of mesh updating and remeshing are no longer needed; (2) The topological derivative is calculated for the iterative position of new holes into the design domain, which can completely solve the initial layout dependency problem and significantly reduce the number of design variables; (3) New concepts related to the topological derivative threshold and the influence region of inserted holes are defined to adaptively adjust the inserting frequency and inserting position of new holes, and the numerical stability of topology optimization could then be kept very well; (4) The smoothly deformable implicit curve (SDIC), which is characterized by very few parameters and high deformation capacity, is utilized to describe the hole boundary, since SDIC could facilitate the fixed-grid analysis as well as the merge process of holes. The structural optimization based on ABM is essentially a collaborative design process that contains the shape optimization of inserted holes as well as the topology changes caused by the insertion of new holes and the merging/separation of inserted holes. Theoretical analysis and numerical results showed that ABM can be implemented conveniently thanks to the adoption of the FCM/SDIC framework, and the optimized results featured by clear and smooth boundaries could be obtained with much less number of design variables by using ABM. Namely, the proposed ABM retains all the advantages of the traditional bubble method, while effectively breaking through its development bottleneck caused by the use of lagrangian description and the parametric B-spline curve.

2019, 51(4): 1235-1244. doi: 10.6052/0459-1879-18-455

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STUDY ON FRACTURE TOUGHNESS OF MODE I OF SHALE BASED ON MICRO-MECHANICAL TEST

Han Qiang, Qu zhan, Ye Zhengyin, Dong Guangjian

Fracture toughness of mode I ($K_{IC})$ is one of the important mechanical parameters for hydraulic fracturing of shale gas reservoir. Due to the heterogeneity of shale composition, the conventional mechanical measurement has some problems such as large sample volume, discontinuous mechanical interpretation parameters, and low interpretation accuracy. One of the challenges is to obtain the fracture characteristics of shale in time to ensure the safety and efficiency of engineering construction. In this paper, research on fracture toughness of mode I of shale is performed based on micro-indentation. It can be used to study the mechanism of shale micro-crack initiation, development and formation of macro-crack, and to predict the macro-parameters of shale. Based on the analysis of multi-scale composition of shale, the fracture toughness tests with pyramid indenter (Vickers indenter and Berkovich indenter) were performed by micro-indentation. The relationship between residual indentation and indenter was evaluated, and the effect of experimental load on shale micro-fracture was analyzed. The optimization of indenter parameter also was discussed. The fracture toughness of shale is evaluated at meso-scale. The applicability of the micro-indentation test was evaluated, based on a comparative analysis with the results of the Brazil disc test. The results show that t the fluctuation of fracture toughness obtained by micro-indentation is slight when load is within the effective range. When load is too large, the fracture toughness of meso-scale is gradually reduced due to local drop-cuts on the indentation area. The average value of $K_{IC}$ obtained by micro-indentation is 0.86 MPa$\cdot \sqrt{m}$,and the average value obtained by Brazilian disc test is 0.92 MPa$\cdot\sqrt{m}$. The heterogeneity of shale composition results in more dispersed meso-mechancial measurement than macroscopic measurement. Micro-indentation test can be used to characterize shale fracture toughness of mode I and perform macroscopic prediction. It provides a new method for effectively solving shale gas hydraulic fracturing.

2019, 51(4): 1245-1254. doi: 10.6052/0459-1879-18-283

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STUDY ON AERODYNAMIC DAMPING OF SEMI-SUBMERSIBLE FLOATING WIND TURBINES

Chen Jiahao, Hu Zhiqiang

Aerodynamic damping effect has an impact on dynamic responses of an offshore floating wind turbine induced by the greater platform motion of an offshore floating wind turbine, which has attracted increasing attention by Chinese and foreign scholars recently. In order to investigate aerodynamic damping effects on an offshore floating wind turbine, a mathematical model of the aerodynamic damping of offshore floating wind turbines is deduced, and then the study on the characteristics of the aerodynamic damping effect of offshore floating wind turbines and the law of the aerodynamic damping effect of offshore floating wind turbines are conducted using model experimental results and simulation results in the paper. The results show that the aerodynamic damping effect of a semi-submersible offshore floating wind turbine in operation condition is greater than that in parked condition. Aerodynamic damping effect restrains the platform surge motion, the platform pitch motion and the nacelle motion of a semi-submersible offshore floating wind turbine in the operation condition. In frequency-domain, aerodynamic damping effect has an impact on motion at its inherent frequency but has little effect on the motion in wave-energy frequency range relating to the wind speed and wave state. The aerodynamic effect of offshore floating wind turbines is in positive correlation with the wind speed, but the gradient of aerodynamic damping effect of a semi-submersible offshore floating wind turbine gradually decreases with the wind speed below the rated wind speed. When the wind speed reach or exceed the rated wind speed, there could be negative damping effect on an offshore floating wind turbine with a blade-pitch-controller. It is found that decreasing proportionality coefficient of the blade-pitch-controller can reduce the sensitivity of the blade-pitch-controller so as to mitigate the negative aerodynamic damping of a semi-submersible offshore floating wind turbine and improve the motion performances of a semi-submersible offshore floating wind turbine to some extent.

2019, 51(4): 1255-1265. doi: 10.6052/0459-1879-18-148

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EXTREME MECHANICS

Zheng Xiaojing

With the continuous development of cutting-edge science and new technologies, the studies on the ultra-conventional scale, density, hardness, stiffness and other properties of engineering materials and structures, as well as their mechanical behavior in extreme environments, such as ultra-conventional temperature, speed, physical and chemical fields, and severe weather, requires more effective theories and methods of mechanics. This presentation starts from the fundamental definition and scientific connotation of extreme mechanics, introduces the research status of extreme mechanics from three aspects: extreme properties, extreme loads, and discipline development, in combination of grand engineering and scientific challenges. The characteristics of extreme mechanics and major challenges in the aspects of mechanical theory, computational methods and experimental techniques are concluded. Prospects for the future development of extreme mechanics are proposed.

2019, 51(4): 1266-1272. doi: 10.6052/0459-1879-19-189

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2019 Vol. 51, No. 4

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