力学学报

REVIEW OF THE APPLICATION OF ATOMIC FORCE MICROSCOPY IN TESTING THE MECHANICAL PROPERTIES OF TWO-DIMENSIONAL MATERIALS

Gao Yang

Graphene and other two-dimensional (2D) materials possess various excellent properties and hold great promises for next generation of electronic devices and other applications. The mechanical properties are of fundamental importance in the research and application of 2D materials. Despite the fact that 2D materials have been extensively investigated in the past two decades, efforts on the mechanical properties are strikingly lacking and vastly needed. Atomic force microscopy (AFM) is one of the most widely used tools for the mechanical characterizations of low-dimensional materials. Particularly, the AFM-based nano-indentation technique has been extensively employed to explore the mechanical properties of 2D materials. In this review, we first introduce the basic backgrounds of 2D materials and atomic force microscopy. The mechanism and theoretical background of AFM-based nano-indentation are then demonstrated. In the second part, we review the research work by employing nano-indentation on studying the in-plane mechanical properties of 2D materials. The measurement errors of AFM-based nano-indentation and their origins are also discussed. Nano-indentation is perfectly suitable for the in-plane/intralayer mechanical measurement but also greatly limited in probing the out-of-plane/interlayer elasticity, due to the extreme anisotropy of 2D materials. Therefore, in the third part, we introduce an unconventional AFM-based technique - Angstrom-indentation which allows for sub-nm deformation on 2D materials. With such a shallow indentation depth comparable to the interlayer spacing of 2D materials, Angstrom-indentation is capable of measuring and tuning the interlayer van der Waals interactions in 2D materials. The interlayer elasticities of graphene and graphene oxide measured by Angstrom-indentation are discussed as examples in the third part. In the final part, we give a quick overview of a new type of 2D material - van der Waals heterostructure and its novel mechanical properties. We also discuss the potential application of Å-indentation in the investigation of the mechanical properties of van der Waals heterostructures.

2021, 53(4): 929-943. doi: 10.6052/0459-1879-20-354

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FLUID-STRUCTURE INTERACTION BETWEEN A HIGH-PRESSURE PULSATING BUBBLE AND A FLOATING STRUCTURE

Hu Zhenyu, Cao Zhuoer, Li Shuai, Zhang Aman

This paper experimentally and numerically investigates the fluid-structure interaction between a spark-induced bubble and a floating structure. The boundary integral method is adopted to simulate the bubble dynamic behaviors and the auxiliary function method is used to improve the computational accuracy of the nonlinear fluid-structure interaction. The double-node method is employed to maintain the computational stability of the gas-liquid-solid interaction line. Besides, we use the underwater electric discharge technique to generate bubbles and the high-speed photography to record the bubble dynamics and the structural responses. Firstly, we compare the numerical result with the experimental data and favorable agreement is achieved which validates this numerical model. Through parametric study with respect to the dimensionless distance $\gamma _{s} $ from the initial bubble center to the floating structure (the reference length is the maximum bubble radius), we then find that (1) as $\gamma_{s} $ increases from 0.2 to 2, five types of jetting pattern such as necking together with annular jet ($0.2\leqslant \gamma_{s} \leqslant 0.3)$, contacting jet ($0.4\leqslant \gamma_{s} \leqslant 0.6)$, non-contacting jet ($0.7\leqslant \gamma_{s} \leqslant 1)$, collision of a jet directed towards the floating body and a counter-jet ($1.1\leqslant \gamma_{s} \leqslant 1.3)$ and individual counter-jet ($1.4\leqslant \gamma_{s} \leqslant 2)$ can be formed; (2) it is also found that the velocity of the jet directed towards the structure first increases, then decreases and finally increases again as $\gamma_{s} $ increases; additionally, it may be in the order of $\sim$1000m/s when $\gamma _{s} $ varies from 0.7 to 0.9; as $\gamma_{s} $ increases, the counter-jet velocity increases; (3) under the conditions of the presented experiments, the bubble migrates towards the floating structure when $\gamma_{s} <\mbox{1.5}$ due to the stronger Bjerknes attraction of the floating structure than the Bjerknes repellence of the free surface on the bubble during the collapsing phase. When $\gamma_{s} \geqslant \mbox{1.5}$, however, the free surface has stronger effects on the migratory behavior of the bubble than the floating structure which causes the bubble to migrate away from the free surface at the collapse stage.

2021, 53(4): 944-961. doi: 10.6052/0459-1879-20-357

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BUBBLE SLIPPING ON A SUPERHYDROPHOBIC PLANAR STRAIGHT TRAJECTORY UNDER DIFFERENT SURFACE ORIENTATIONS

Ye Yuhang, Tu Chengxu, Bao Fubing, Wang Yukun, Yang Sensen

Bubble directional transportation using the superhydrophobic surfaces of different specific geometry in the water has broad application prospects in the fields of mineral flotation and biological incubation. The surface orientation of the planar straight superhydrophobic surfaces is a crucial parameter for the related engineering structures. However, it is still unclear that the effect of surface orientation on the bubble slipping along the inclined surface. The high-speed shadowgraphy is used to study the movement characteristics of the slipping bubble ($D_{eq}=2.4$ mm, $Re=500$ $\sim$ 700, $We=7$ $\sim$ 13) on the superhydrophobic linear trajectory with the width of 2 mm under different surface orientations ($-90^\circ\leqslant \beta \leqslant 90^\circ$) and inclination angles ($45^\circ\leqslant \alpha \leqslant 75^\circ$). The slipping velocity of the bubble ($u)$ on the trajectory is approximately stable, and the shape like semi-bullet with multi-ridges. The slipping bubble can be divided into two shape types: the stable and the unstable according to the fluctuation level of the gas-liquid interface. Stable bubble only appear when the inclination angle is small and the azimuth angle is large ($45^\circ\leqslant \alpha <70^\circ$, $| \beta | \geqslant 45^\circ$). As $\alpha $ changes, two kinds of $u$-$\beta $ relations can be found: When $\alpha \leqslant 65^\circ$, the slipping velocity is approximately a unimodal distribution about $\beta =0^\circ$ (the maximum sliding velocity at $\beta =0^\circ$); When $\alpha \geqslant 70^\circ$, the azimuth angle has no significant influence on $u$. The maximum sliding velocity can be upto 0.66 m/s ($\beta =0^\circ$, $\alpha =70^\circ$), which is much higher than that of the free-rising bubble of the similar size ($\sim$0.25 m/s), mainly as a combined effect of the wall-wettability and the inertial force. Surface orientation ($\beta$) and trajectory inclination angle ($\alpha$) affect the slipping velocity and the stability of the gas-liquid interface by changing the driving force, as a buoyance component, of the bubble along the trajectory direction and the bubble frontal area.

2021, 53(4): 962-972. doi: 10.6052/0459-1879-20-405

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NUMERICAL STUDY ON WATER-AIR TWO-PHASE FLOW BASED ON WENO-THINC/WLIC MODEL

Wei Zhilong, Jiang Qin

Water-air two-phase flow can be found in many practical engineering projects in various fields. To simulate water-air two-phase flow with high accuracy has always been a challenging problem and a highlight in the realm of computational fluid dynamics. Based on the assumption that both water and air can be considered as incompressible fluid, for free surface flow in open water areas, the WENO-THINC/WLIC model for water-air two-phase flow is therefore established. In the developed model, the fifth-order accurate weighted essentially non-oscillation (WENO) scheme is used to solve the Navier-Stokes equation for fluid flows, and the improved multi-dimensional tangent of hyperbola for interface capturing scheme with weighted line interface calculation method (THINC/WLIC) is adopted to track the interface. The fractional step method is applied to discretize and solve the governing equations, the pressure projection method is adopted to compute the pressure field, and the third-order accurate total variation diminishing (TVD) Runge-Kutta (RK) method is used to discretize the temporal terms. In order to verify the model, it is applied to simulate two benchmarks of interface evolution subjected to an external velocity field, Zalesak's disk and shearing vortex, the linear sloshing, and the dam-breaking flow problem. Through comparison of the simulated results with the analytical or experimental ones, adaptability and accuracy of the water-air two-phase model are discussed. The analysis indicates that the simulation outputs are in good accordance with theoretical or experimental results, which means the model is capable to simulate incompressible water-air two-phase flows. With the further improved WENO schemes and THINC schemes, more precise prediction results for water-air two phase flow problems can be achieved with the proposed combined WENO-THINC model.

2021, 53(4): 973-985. doi: 10.6052/0459-1879-20-430

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A MONOLITHIC METHOD FOR SIMULATING CONJUGATE HEAT TRANSFER VIA QUASI-IMPLICIT SCHEME OF CHARACTERISTIC-BASED SPLIT FINITE ELEMENT

Liu Yu, Deng Jiayu, Wang Chengen, Su Hongxin

Conjugate heat transfer is widely present in the fields of science and engineering. With the development of computing power, the accurate and effective numerical simulation of conjugate heat transfer has become a major challenge in scientific research and engineering design. The method of numerical simulation of conjugate heat transfer can be divided into two main categories: partitioned method and monolithic method. Each of these methods has its pros and cons. We have developed a monolithic method for simulating the conjugate heat transfer between solid and incompressible laminar flows with the finite element method. Heat conduction in solid is solved by the standard Galerkin finite element method. The flow solution adopts the characteristic-based split finite element method (CBS). This method is an important finite element method for solving flow problems, and equal-order finite elements can be used. Compared with semi-implicit and CBS-AC schemes, the quasi-implicit scheme of this method can adopt a larger time-step. The stability of the quasi-implicit scheme is improved by distinguishing the time step in the stabilization item from the global time step. Based on the quasi-implicit scheme of the improved CBS method, a monolithic method of conjugate heat transfer numerical simulation has been developed. In this way, the fluid part and solid part of the computational domain can be divided into finite element meshes as a whole, and the equal-order interpolation functions can be used for all variables, thus facilitating the realization of the program. The accuracy of this method is validated by simulating the benchmark problems. The effect of the time step for the solid domain on the convergence of steady conjugate heat transfer simulation has also been studied.

2021, 53(4): 986-997. doi: 10.6052/0459-1879-20-299

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STUDY ON ROTATIONAL VISCOSITY OF NEMATIC LYOTROPIC LIQUID CRYSTAL

Chen Lingfeng, Yu Jiajia, Li Yourong, Huang Yingzhou, Li Guyuan

Lyotropic liquid crystal exhibits excellent biocompatibility, non-toxicity, biodegradability, optical anisotropy, and electromagnetic anisotropy. It has been widely used in the areas of biology, medical engineering and liquid crystal displaying, such as cell interaction, nerve stimulation transmission, fat absorption and intelligent drug transport. In this paper, the rotational viscosity of the lyotropic liquid crystal Sunset Yellow in the nematic phase at different temperature and solution concentration is measured by the rotating magnetic field method. Combined with the self-assembly process of lyotropic liquid crystal molecules, the variation of rotational viscosity of lyotropic liquid crystal in the nematic phase with temperature and solution concentration is analyzed theoretically. The results show that the rotational viscosity of the lyotropic liquid crystal is positively correlated with the square of the average length of the self-assembled columns, increasing with the increase of concentration, but decreasing exponentially with the increase of temperature. The empirical expression of rotational viscosity related to temperature and concentration of nematic lyotropic liquid crystal is constructed. The calculated results of the empirical expression are in good agreement with the experimental values, with the maximum error of 18.56${\%}$. A new indirect method of obtaining the shear energy of lyotropic liquid crystal by using rotating rheometer is proposed. The shear energy of lyotropic liquid crystal increases with the increase of solution concentration, but it is hardly related with the change of temperature in the experimental range. The shear energy obtained in this paper is in good agreement with the results of Joshi et al. who used the X-ray detection method, with the maximum error of 3${\%}$. The influence of length-diameter ratio of the columns on the rotational viscosity is investigated by using the variation of self-assembly capacity of liquid crystal molecules with temperature. The "one-step method" measurement is proposed, which greatly reduces the expenses and complexity of related experimental researches.

2021, 53(4): 998-1007. doi: 10.6052/0459-1879-20-272

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EFFECTS OF WETTABILITY ON DISPLACEMENT EFFICIENCY OF TWO-PHASE FLOW IN POROUS MEDIA

Wei Guanju, Hu Ran, Liao Zhen, Chen Yifeng

Displacement efficiency and displacement pattern of multiphase flow in porous media have a profound influence on many geo-energy applications such as geologic CO$_{2}$ sequestration and enhanced oil recovery. Wettability is one of the most important factors affecting the displacement pattern and displacement efficiency of multiphase flow in porous media. Here, we combined the glass microfluidics, inverted microscope and high speed CMOS camera to set up a visualization experimental system and modified the surface wettability of the glass microfluidics by using the silanization treatment and piranha solution. Pore-scale visualization displacement experiments were conducted on five flow rates and two wetting conditions (hydrophilic and hydrophobic conditions) in glass microfluidics which are fabricated from the pore structure of natural sandstone. Experimental results show that the displacement pattern shifts from capillary fingering to compact displacement pattern both in the hydrophilic and hydrophobic media as the flow rate increases. Under lower flow rates, the capillary force plays the dominant role in the fluid invasion processes. The invasion finger width and the number of air clusters in hydrophilic media are both smaller than those in the hydrophobic media, but the maximum air cluster radius, the average cluster radius and the standard deviation of cluster radius are all greater under hydrophilic conditions. The results also demonstrate that the displacement efficiency under hydrophilic condition is significantly lower than that of hydrophobic conditions due to single-channel flow and "by pass" flow phenomena which both only occur in hydrophilic media. Finally, a modified capillary number was introduced in order to consider the role of wettability (contact angle) under favourable displacement. Then, a relationship between the displacement efficiency and the modified capillary number was proposed, which provides a potential and useful method for the prediction of displacement efficiency under different wetting conditions during favourable displacement.

2021, 53(4): 1008-1017. doi: 10.6052/0459-1879-20-403

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WAVE-INDUCED FORCE ON FLEXIBLE MARSH PLANTS

Zhang Xiaoxia, Lin Pengzhi

Salt marshes are common features in coastal regions and forming eco-rich wetlands. These wetlands provide ecosystem services, tourism and fishery benefits, as well as coast protection. Salt marshes can dissipate wave energy, which enhances coastal stability and protects the shoreline from storms and small tsunami waves. Previous wave damping predicting methods are usually oversimplified by modeling plants as rigid cylinders. Further, these studies strongly depend on the adjustment of empirical drag coefficient, while a knowledge gap exists between the mechanism of flexible plant-wave interaction. A marsh plant usually consists of multiple flexible leaves and a less flexible central stem, both the geometric and flexibility of the leaves and the stem affect the drag on the full plant. Under waves, the leaves and the stem reconfigure to different degrees at different speeds. The dynamic response of plant elements reduces the relative velocity between the wave and the plant. Further, the leaves and the stem interact with one another, making the characteristics of wave-induced plant force highly complicated. Build on the force scaling law for a simple plant element, such as a flat leaf or a cylindrical stem, we proposed a simple equation to predict the drag on plants with both leaves and stem. The force on the full plant is the sum of the force on the leaves and the force on the stem. The force on a representative leaf and the stem were estimated by the force scaling law. The force due to all the leaves was estimated by the force on the representative leaf using a sheltering coefficient, which accounts for the drag reduction in the leaves due to the interaction between the leaves and the stem. The model predicted maximum drag and the drag force over the wave period agreed well with the experiment measured drag force on an individual leaf, an individual stem, and model and live plants with both leaves and stem.

2021, 53(4): 1018-1027. doi: 10.6052/0459-1879-20-429

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HYPERELASTIC MODEL WITH ENTANGLEMENT EFFECT

Xiao Rui, Xiang Yuhai, Zhong Danming, Qu Shaoxing

Classic hyperelastic models, such as the Neo-Hookean model and Arruda-Boyce eight-chain model, have been widely adopted to describe the mechanical response of rubbers. However, the experimental data has shown that using a single set of parameters these models have difficulty in accurately predicting the measured stress-strain relationship of rubbers under various loading modes. For example, the Arruda-Boyce model fails to describe the stress response in biaxial loading conditions of Treloar's classic experiments. To address this limitation, this work develops a hyperelastic theory incorporation the entanglement effect. At the microscale, the Langevin statistical model is adopted for the entropic part and the tube model is used for the entanglement part. The affine assumption is used to construct the micro-macro mapping. Macroscopically, the Helmholtz free energy of the model consists of both an entropic part and an entanglement part. The entropic part has the same form as the eight-chain model, depending on the first invariant of the Cauchy-Green deformation tensor. In contrast, the entanglement part is a function of the second invariant of the Cauchy-Green deformation tensor. Compared with the eight-chain model and Neo-Hookean model, the developed model with three parameters provides a greatly improved prediction on the experimentally measured stress response of rubbers in uniaxial, pure shear and equibiaxial loading conditions, as well as that of biaxial tension tests with different pre-stretch ratios. The model shows superior prediction ability compared with the classic models, such as the Neo-Hookean model, the eight-chain model, the Yeoh model and the generalized Rivlin model. Finally, the work also compares the free energy density of entanglement part developed in this work and those of the related models in the literature. The constitutive theory developed in this work can accurately predict the large deformation behaviors of rubbers and other related soft materials, which can potentially benefit their engineering applications.

2021, 53(4): 1028-1037. doi: 10.6052/0459-1879-21-008

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ANALYSIS OF 2-D ORTHOTROPIC POTENTIAL PROBLEMS USING FAST MULTIPOLE BOUNDARY ELEMENT METHOD WITH HIGHER ORDER ELEMENTS

Li Cong, Hu Bin, Hu Zongjun, Niu Zhongrong

A new fast multipole boundary element method is proposed for analyzing 2-D orthotropic potential problems by using linear and three-node quadratic elements. In the fast multipole boundary element method, fast multipole expansions are used for the integrals on elements that are far away from the source point, and the direct evaluations are used for the integrals on elements that are close to the source point. The use of linear and three-node quadratic elements results in more complicated computations for near-field integrals, especially singular integrals and nearly singular integrals. In this paper, the complex notation is introduced to simplify the near-field integrals. If the boundary is discretized by linear elements, the near-field integrals are calculated by the analytic formulas, if the three-node quadratic element is used, a semi analytical algorithm is given to calculate the near-field integrals. Accurate evaluations of the singular integrals and nearly singular integrals on linear and three-node quadratic elements ensure that the present fast multipole boundary element method can be applied to the ultra-thin structure, which broadens the application of the fast multipole boundary element method with linear and quadratic elements. Numerical examples show that the number of elements required by the fast multipole boundary element method with linear and quadratic elements is significantly less than that with constant elements. In addition, the required CPU time is increased linearly with the increase of the number of degrees of freedom $(N)$, which demonstrates the computational efficiency is still in the complexity of $O (N)$. Therefore, the present method exhibits higher accuracy and efficiency for solving large-scale problems.

2021, 53(4): 1038-1048. doi: 10.6052/0459-1879-20-455

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BOUNDARY ELEMENT ANALYSIS OF COMPLEX STRESS INTENSITY FACTORS OF BIMATERIAL INTERFACE CRACKS

Gu Yan, Zhang Yaoming

The asymptotic crack-tip field for bimaterial interface cracks exhibits an oscillatory behavior which is quite different from that for cracks in homogeneous materials. Modeling such interface cracks by the conventional solution procedures designed for homogeneous materials is inadequate, and may not lead to accurate solutions. This paper introduces a new set of novel special crack-tip elements for analysis of interface cracks in linear elastic bimaterials by using the boundary element method (BEM). The method can properly describe the oscillatory displacement and stress fields in the vicinity of the interfacial crack-tip. Furthermore, the troublesome nearly-singular integrals, which are crucial in the application of the BEM for ultra-thin structural problems, are calculated accurately by using a nonlinear coordinate transformation. Accurate and reliable BEM results with only a small number of boundary elements can be obtained for interface crack analysis of ultra-thin composite bimaterials.

2021, 53(4): 1049-1058. doi: 10.6052/0459-1879-20-440

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A STUDY ON MICRO-MACRO MECHANISMS OF CRACK NUCLEATION DURING CREEP IN BRITTLE ROCKS

Li Xiaozhao, Jia Yaxing, Zhang Qishuo, Qi Chengzhi

The creep behaviours influenced by the growth, coalescence and nucleation of microcracks in brittle rocks have an essential meaning for evaluating the microseismicity and rock bursts of the surrounding rocks in deep underground engineering. However, the micro-macro mechanisms of the damage catastrophe from the crack nucleation effect on the total creep behaviour of brittle rocks are rarely studied. In this study, based on the subcritical crack growth model, the damage model relating to the crack, strain and acoustic emission events, and the function of the damage path influenced by crack nucleation, a micro-macro model is proposed to explain the effect of crack nucleation on creep of brittle rocks. The function of the damage path influenced by crack nucleation is defined by the parameters of the size of damage catastrophe (i.e., $\Delta D_{CN}$) and the time difference (i.e., $\Delta t$) between the adjacent crack nucleations. The damage and time parameters in this proposed function of the damage path can be determined by the use of the experimental data of acoustic missions. The rationality of this proposed micro-macro model is verified by comparing the experimental results. The effects of the damage catastrophe size from crack nucleation, the happened time of crack nucleation, and the number of crack nucleation on the crack length, crack velocity, axial strain, and axial strain rate are discussed during creep of brittle rocks. The suggested model provides a certain theoretical help for the more reasonable, economical, and efficient construction of deep underground engineering.

2021, 53(4): 1059-1069. doi: 10.6052/0459-1879-20-400

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ADDITIVE MANUFACTURING-ORIENTED STRESS MINIMIZATION TOPOLOGY OPTIMIZATION WITH CONNECTIVITY

Wang Chao, Xu Bin, Duan Zunyi, Rong Jianhua

The organic combination of additive manufacturing and topology optimization will greatly promote the development of high-performance products. However, most of the existing researches on design performance and manufacturability based on topology optimization are carried out separately. And, they often focus on traditional stiffness problems and lack the consideration of the most important strength problems in practical engineering. In this paper, an additive manufacturing-oriented topology optimization model for the structural optimization problem that considers strength and manufacturability connectivity collaboratively is established, viz, a structural stress minimization under material volume and connectivity-based scalar field constraints. An effective optimization strategy is introduced to overcome various numerical problems in the solution. The P-norm based global scalar field constraint measure is employed, together with the stability transformation method-based error correction technique to realize the effective control of the local scalar field. The corresponding sensitivity is derived in detail. The rationality and effectiveness of the proposed model and method are demonstrated by typical numerical examples. Optimized results show that the stiffness maximization design considering only the connectivity constraint may not necessarily avoid local high stress concentration, and the design is not necessarily equivalent to the stress minimization connectivity design. Sufficient material allowance and appropriate connectivity constraint boundary conditions are important to improve the performance of the design studied. Moreover, the value of the stress aggregation parameter is not the bigger the better, only a reasonable value can help to obtain a high-performance design. To some extent, the results also demonstrate the necessity and feasibility of considering the strength problem in manufacturing-oriented topology optimization.

2021, 53(4): 1070-1080. doi: 10.6052/0459-1879-20-389

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DYNAMIC COUPLED THERMO-HYDRO-MECHANICAL PROBLEM FOR SATURATED POROUS VISCOELASTIC FOUNDATION

Guo Ying, Li Wenjie, Ma Jianjun, Liang Bin, Xiong Chunbao

Natural soil often has the characteristics of rheology due to different depositional conditions and stress states. The present paper focuses on investigated the effects of different porosity and permeability coefficient in saturated porous foundation which considered the viscoelastic relaxation times with coupled thermo-hydro-mechanical fields under external load. A two-dimensional coupled thermo-hydro-mechanical dynamics problem for a half-space on an isotropic, uniform, fully saturated, and poroviscoelastic soil (THMVD) whose surface is subjected to either mechanical force or thermal load based on the Biot's wave theory of porous media, Darcy's law, and Lord-Shulman (L-S) generalized thermoelastic theory with Kelvin-Voigt viscoelastic model is investigated. The general relationships among the non-dimensional vertical displacement, excess pore water pressure, vertical stress, and temperature distribution are then deduced via normal mode analysis and depicted graphically. Normal mode analysis is a method using weighted residuals to derive analytical solutions. Via this method, the equation can be divided into two parts without integral transformation and inverse transformation, thereby increasing the speed of decoupling and eliminating the limitation of numerical inverse transformation. The effects of the porosity and the permeability coefficient on the four different physical variables have been investigated. It can be shown that: whatever load is being considered, the variation of load frequencies have obvious effect on all the considered physical variables; the porosity and permeability have the most obvious influence on non-dimension excess pore water pressure. When thermal loads were considered only, the variation of porosity and permeability coefficient had barly effect on non-dimension temperature. This proposed derivation method can be widely applied in the geotechnical engineering field, especially with regard to the mechanical and thermal behaviors of commercial buildings, high-speed railways, and highway energy foundations. The research results of this problem can lay a certain theoretical foundation for engineering construction and have a certain guiding significance.

2021, 53(4): 1081-1092. doi: 10.6052/0459-1879-20-385

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ACTIVE VIBRATION CONTROL OF A ROTATING BLADE BASED ON MACRO FIBER COMPOSITE

Zhang Bo, Ding Hu, Chen Liqun

For a long time, blade vibration failure occupies a quite large proportion of the total failure of the complete aeroengine. Developing the vibration reduction technology is of great importance for reducing the weight, improving the performance and extending the life for the rotating blade structure. In the present paper, the active vibration control is investigated in the presence of the 2:1 internal resonance of a pre-deformed rotating blade through introducing the sensors and actuators made of macro fiber composite (MFC). The equations of motion of the proportional-derivative feedback closed-loop control system are established with the effects of the time delay. The evolution equations of the controlled system are derived via the perturbation analysis. The effects of the velocity gain, the displacement gain, the time delay and some other system parameters on the steady-state response and the stabilities of the controlled system are revealed by the application of the continuation method. The analytic solutions are in good agreement with those obtained from the numerical integration. The main findings of the present study are as followings: the time delay has a significant effect on the stabilities of the controlled system. When the time delay exceeds a certain value, the equilibrium points of the evolution equations lose their stability. At the same time, the closed-loop control system enters a new period motion with a large vibration amplitude. There exists a range of displacement gain in which the multi-valued phenomenon appears in the steady-state response of the controlled system. Moreover, the straight borderline between the stable and the unstable regions in the gains plane is destroyed due to this range. Inappropriate assignments of the velocity gain and the displacement gain will cause a new resonance in the close-loop control system. The research results lay the theoretical foundations for the vibration reduction of the blade structure.

2021, 53(4): 1093-1102. doi: 10.6052/0459-1879-20-448

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PARAMETRIC AEROELASTIC MODELING OF FOLDING WING BASED ON MANIFOLD TANGENT SPACE INTERPOLATION

Zhan Jiuyu, Zhou Xinhua, Huang Rui

The parametric aeroelastic modeling of a morphing aircraft is a hot topic in the research field of morphing aircraft design. However, the traditional non-parametric aeroelastic dynamic modeling methods have some problems, such as low modeling efficiency and complex aeroelastic analysis for for aeroelastic research of morphing aircraft with structural parametric characteristics. In this paper, a parametric aeroelastic modeling method of folding wing based on the tangent space interpolation is proposed. Firstly, based on the structural finite element models of a folding wing at several folding angles, a parametric structural dynamic model of the folding wing is established by tangent space interpolation. Then, the parametric unsteady aerodynamics is computed by the Doublet Lattice method. At last, the parametric aeroelastic model of the folding wing is obtained by coupling the structural dynamics and unsteady aerodynamics. To verify the accuracy of the parameterized model in the aeroelastic calculation, a small aspect ratio folding wing is taken as the research object. The dynamic characteristics including the natural frequencies, mode shapes, and flutter boundaries at different folding angles are efficiently calculated. In addition, the numerical results computed via the present parametric method are compared with the direct non-parametric method. The demonstration shows that the results from the parametric aeroelastic model is consistent with the direct method for the aeroelastic problems and has the advantage of higher calculation efficiency.

2021, 53(4): 1103-1113. doi: 10.6052/0459-1879-20-376

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STUDY ON THE BANDGAPS OF DEFECT STATES AND APPLICATION OF ENERGY HARVESTING OF LOCAL RESONANT PHONONIC CRYSTAL PLATE

Lu Yiming, Cao Dongxing, Shen Yongjun, Chen Xumin

A local resonant phononic crystal plate, which is composed by quadrangular epoxy resin matrix embedded with cylindrical scatterers, is proposed to study the vibration energy harvesting performance. The bandgaps and energy concentration characteristics for the defect state structure are analyzed in detail. Firstly, the bandgap curve and energy transmission characteristics are analyzed for perfect and point defect phononic plate with 5 $\times$ 5 array structure based on supercell theory and finite element method. Considering the energy concentration characteristics of the point defect local resonance phononic crystal structure, piezoelectric material is used to replace the scatterer material of defect point, and the vibration energy characteristics are then analyzed. The results show that it has narrow resonance frequency band for the 5 $\times$ 5 point defect supercell structure. In order to improve the energy capture efficiency, two kind of new phononic crystal plate composed of three 5 $\times$ 5 supercells with different defect numbers and layout are proposed as the vibration energy harvester. According to the results of the electromechanical coupling analysis, it shows that the proposed local resonant phononic crystal plate overcomes the disadvantages of the single point defect supercell structure, such as too few defect modes and too narrow resonance frequency band. The working frequency band of the energy harvester is widened and the output voltage is increased. Additionally, it can further broaden the energy harvesting bandwidth and achieve better efficiency by introducing different number and configuration of defect states.

2021, 53(4): 1114-1123. doi: 10.6052/0459-1879-20-436

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NONLIEAR BENDING WAVES OF A PIEZOELECTRIC LAMINATED BEAM WITH ELECTRICAL BOUNDARY

Zhao Xining, Yang Xiaodong, Zhang Wei

Nonlinear science has been an important symbol in the development of modern science, especially the researches in nonlinear dynamics and nonlinear waves have extraordinary significance in solving the complex phenomena and problems encountered in various fields of natural science. In this paper, the nonlinear bending wave propagation of a piezoelectric laminated beam with electrical boundary conditions is studied. Firstly, considering the geometric nonlinear effect and piezoelectric coupling effect, the nonlinear equation of the one-dimensional infinite rectangular piezoelectric laminated beams is established by using Hamiltonian principle. Secondly, the Jacobi elliptic function expansion method is used to treat the nonlinear flexural wave equation, and the corresponding shock wave solution and solitary wave solution of the nonlinear flexural wave equation are obtained in the approximate case. Last, the nonlinear Schrodinger equation is obtained by using the reduced perturbation method, and the bright and dark soliton solutions are further obtained. Moreover, the effects of external voltage and the thickness of the piezoelectric layer on the characteristics of shock wave and solitary wave as well as bright and dark solitons are studied. The results show that when the wave velocity is small, the external voltage has a great influence on the shock wave, and when the wave velocity is large, the external voltage has no effect on the solitary wave. The bright solitons and the dark solitons can be obtained by adjusting the external voltage applied to the piezoelectric laminated beam. It is found that the amplitudes of bright and dark solitons increase with the increase of external voltages.

2021, 53(4): 1124-1137. doi: 10.6052/0459-1879-20-409

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A ROBUST STABILIZATION CONTROL FOR DUAL-ARM SPACE ROBOT CAPTURING TUMBLING TARGET

Xia Pengcheng, Luo Jianjun, Wang Mingming

Due to the inaccurate inertia parameters of the captured tumbling target and the internal wrenches at the grasping points, the motion of the space robot stabilizing the tumbling target cannot be planned and controlled effectively in the post-capture phase. In the existing studies, it is risky to track the desired trajectory planned by inaccurate parameters, which cannot restrain the contact wrenches and guarantee the safety of the grasping points. In order to control the post-capture dual-arm space robot safely, a robust control scheme is proposed for the dual-arm space robot capturing a tumbling target in this paper, where the influences of the inaccurate target inertia parameters and the internal wrenches at the grasping points are considered. First, a robust invariant set is constructed considering the influences of the inaccurate target parameters and internal stress wrenches. Then, to plan a safe desired motion for the dual-arm space robot, a virtual robust control law for the captured target is developed, where the desired trajectory of the target is planned within the constructed invariant sets. By the motion constraints between the space robot and the target, a robust desired trajectory of the dual-arm space robot is obtained. A barrier Lyapunov function based constrained controller is developed to track the robust trajectory efficiently. By tracking the robust trajectory with prescribed control performance, the designed virtual control law is applied to stabilize the captured target. During the stabilization control process, the measured contact wrenches can be restrained by the proposed scheme effectively, which guarantees the safety of the grasping points and the reliability of the stabilization control. The effectiveness of the proposed scheme is validated via the digital simulations, where a non-cooperative tumbling target is stabilized by a dual-arm space robot.

2021, 53(4): 1138-1155. doi: 10.6052/0459-1879-20-449

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RESEARCH ON OBLIQUE IMPACT OF ROTATING OF FLEXIBLE BEAM BASED ON CONTACT CONSTRAINT METHOD OF LUGRE FRICTION MODEL

Fan Jihua, Gu Tongshun, Wang Mingqiang, Shen Hong, Chen Liwei

Based on the contact constraint method and LuGre friction model, the dynamic problem of oblique impact with friction between a flexible beam system and a slope is studied. The rigid-flexible coupling multi-body system dynamics theory is used to discretize and model the flexible beam with large overall motion, at the beginning of the impact, the impulse-momentum method is used to calculate the jumping velocity, and then the contact constraint is introduced in the normal direction to solve the impact force, in tangential direction, LuGre friction model is used to solve the friction force in two ways, the first is that the friction force is calculated by friction coefficient and collision force when sliding, and introducing tangential constraint to calculate Lagrange multiplier response actual friction force, according to the stick / slip switching judgment, the friction force in the impact process is calculated (which is consistent with that calculated by Coulomb friction model); the second method is to calculate the friction force according to friction coefficient of LuGre friction model and normal collision force, so there is no need to switch between stick and slip during impact, and the same friction calculation formula is used. Compared with Coulomb friction model, LuGre friction model is more accurate in describing the tangential friction process. There is no difference between the two LuGre friction model modeling methods to describe the impact dynamics. Therefore, it shows that the establishment of normal contact constraint and LuGre friction model can meet the collision un-embedding situation to avoid stick slip switching and to describe the relatively accurate advantages of friction.

2021, 53(4): 1156-1169. doi: 10.6052/0459-1879-20-350

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NUMERICAL STUDY ON THERMAL DESTRATIFICATION IN LARGE SCALE HYDROGEN PROPELLANT TANK IN SPACE BY JET INJECTION UNDER ZERO GRAVITY CONDITION

Guo Bin, Zhao Jianfu, Li Kai, Hu Wenrui

Liquid Hydrogen plays a vital role in the future energy system as a space propellant, but it is sensitive to heat leakage from the environment because of its low boiling point and easy evaporation. On the other hand the buoyancy convection in the space microgravity environment is significantly reduced. When there is local heat leakage on the wall of the propellant tank, temperature stratification arises around the heat leakage source causing local overheating. It seriously affects the multiphase heat and mass transfer in the propellant tank which induces the tank pressure rise and jeopardize the structural safety of the system. To prevent the tank pressure from rising above the design of limits, venting or active pressure control techniques must be implemented. The cryogenic jet mixing is an effective means to suppress temperature stratification. The cryogenic fluid is mixed with the fluid inside the tank through a jet nozzle to reduce the local high temperature and achieve uniform temperature. In present paper, the thermal stratification phenomenon caused by the local heat leakage under microgravity condition was numerically simulated by using a fully filled two-dimensional large scale tank model. This paper mainly analyzes the suppression and elimination of local thermal stratification caused by heat leakage near the bottom of the storage tank and the outlet connecting section. The influence of different cryogenic jet mixing conditions on eliminating the temperature stratification effect is analyzed. The results show that the position of jet nozzle has no obvious effect on the elimination of thermal stratification inside the tank when the circular jet nozzle is used and the cryogenic jet condition is the same. When the jet nozzles are located in the same relative position inside the tank and the incident flow rate is the same, the circular jet nozzles have more concentrated flow direction, the flow field in the tank evolves faster, so the thermal stratification elimination effect is better than the hemispherical jet nozzles.

2021, 53(4): 1170-1182. doi: 10.6052/0459-1879-20-343

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APPLICATION OF GENERALIZED FINITE DIFFERENCE METHOD IN ACOUSTIC ANALYSIS OF CAVITY WITH IMPEDANCE BOUNDARY

Chen Zengtao, Wang Fajie, Wang Chao

Acoustic analysis plays significant role in engineering calculations such as noise control and indoor sound insulation. Since the practical acoustic problems usually involve sound-absorbing materials, it is very necessary to analyze acoustic problems with impedance boundary conditions. The generalized finite difference method is a new mesh-less numerical discretization method, this method is based on Taylor series expansion of multivariate function and weighted least square, the partial derivatives of unknown values in the governing equation are expressed as a linear combination of function values at supporting nodes. In this paper, the generalized finite difference method is applied to the analysis of cavity acoustics with impedance boundary conditions firstly, and the corresponding numerical discrete scheme is established. Compared with traditional algorithms, the developed numerical model is a local meshless method with the merits of being mathematically simple, numerically accurate and easy to large-scale acoustic analysis. A benchmark numerical example with analytical solution is examined to verify the influence of the total number of nodes and the number of local supporting nodes on the numerical results, and to obtain an empirical formula of the relationship between maximum computable frequency and node spacing. In addition, the generalized finite difference method is applied to two-dimensional and three-dimensional complex acoustic models without analytical solutions, and is compared with the FEM solutions obtained by COMSOL Multiphysics. Numerical experiments demonstrate that the generalized finite difference method is an efficient, accurate, stable and convergent numerical method, and has broad application prospects in the acoustic analysis of cavities with impedance boundaries.

2021, 53(4): 1183-1195. doi: 10.6052/0459-1879-20-311

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SIMULATION OF BEHAVIOUR OF TYPICAL CONCRETE SPECIMEMS BASED ON A NONLOCAL MACRO-MESO-SCALE CONSISTENT DAMAGE MODEL

Ren Yudong, Chen Jianbing

Concrete is a typical quasi-brittle material, and the nonlinear analysis and crack simulation of concrete during loading are still challenging issues. Classical fracture mechanics and damage mechanics describe crack topology from discrete and continuous perspectives respectively, and became two of the most powerful tools for solid crack simulation and prediction problems. Since the beginning of this century, in the phase field theory and peridynamics significant progress has been made in predicting the crack initiation and propagation and nonlinear analysis. Recently, a new nonlocal macro-meso-scale consistent damage (NMMD) model has been developed based on the basic ideas of phase field theory and peridynamics. In this model, the concepts of material point pair are introduced to characterize the meso-scale damage due to deformation. Then the topologic damage which quantifies the degree of discontinuity in macroscopic solid is defined as the weighted average of meso-scale damage in the influence domain. Through the physically-based energetic degradation function which bridges the topologic damage and energy dissipation, the topologic damage can be inserted into the framework of continuum damage mechanics, which allows this model to simulate the crack process naturally while performing nonlinear analysis without prescribed initial crack and potential propagation path. The present paper takes into account the spatial variability of the meso-scale physical parameters and employs the NMMD model to simulate the whole loading process of typical concrete specimens. The model meso-scale parameters are calibrated through the 1D modeling firstly, and the relationship between the meso-scale parameters and the meso-scale physical-geometric properties of concrete is discussed. Based on the 1D-calibrated parameters, a detailed analysis through the 2D NMMD model is performed. Further, the influence of material parameter spatial variability on the behaviors of uniaxial tensile concrete specimen and notched three-point bending beam is investigated. The work in this paper provides a meaningful reference for the calibration of meso-scale parameters in the NMMD model and the investigation on nonlinear mechanical behavior of concrete and other quasi-brittle materials under complex stress state.

2021, 53(4): 1196-1121. doi: 10.6052/0459-1879-20-427

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MONITORING AND EARLY WARNING EXPERIMENT OF ROCK COLLAPSE

Du Yan, Huo Leichen, Xie Mowen, Jiang Yujing, Jia Beining, Cong Xiaoming

Rock collapse has been a hot issue in the study of geological hazards for many years, and it is difficult to prevent because of its sudden disintegration, which is a serious threaten to human life and property safety. The rock collapse is caused by the dynamic failure of the system instability, so it can be more effective to apply the dynamic monitoring index in early warning. By introducing time-domain dynamic monitoring indicators, the whole process of rock collapse is monitored in real time. Through vibration amplitude, kurtosis index and other indexes, the failure precursor in the detachment phase is analyzed. As the early warning method based on detachment precursor recognition has better timeliness in the early warning of rock collapse, it can realize the early warning of rock block collapse 55 s in advance. The experimental results show that the time-domain dynamic index monitoring can identify the obvious incompatible dynamic response before rock failure, and the variation coefficient has obvious advantages in identifying the oscillation feature. The early warning of collapse disaster can be realized by identifying this oscillation feature. Furthermore, the vibration velocity of rock mass before the collapse is 2.1 times that in the stable phase, and the large impact energy of rock mass at the time of failure is one of the main reasons for the high-speed rockslide. By analyzing the kurtosis index and other time-domain dynamic indexes, the reasonable identification of the failure precursors can be achieved. The study provides new data support and enlightenment for the early warning of rock collapse, the mechanism of rock collapse and the rock movement characteristics after failure.

2021, 53(4): 1212-1221. doi: 10.6052/0459-1879-20-441

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