力学学报

2017, 49(6)

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2017, 49(6): 1-9.

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EXPERIMENTAL INVESTIGATIONS OF STRENGTH, TOUGHNESS AND FAILURE MECHANISM OF THE METAL/EPOXY/METAL ADHESIVE SYSTEM

Li Jingchuan, Liang Lihong, Liu Xiaoming, Ma Hansong, Song Jingru, Wei Yueguang

In the present research, we carry out a systematical experimental investigations on the strength, toughness and failure mechanism of the metal/epoxy/metal adhesive system. For the case of the aluminum alloy cylinder/epoxy/aluminum alloy cylinder adhesive system, we measure the tensile deformation and failure behaviors, including the dependence of the failure loading on the adhesive layer thickness and adhesive interfacial inclined angle. Through introducing a series of definitions, such as average normal stress, average shear stress, average normal strain and average shear strain, along the adhesive interface, we realize the measurements on interfacial failure strength, and obtain the relationship between the interfacial strength and the interfacial adhesive angle as well as adhesive layer thickness, and we further obtain the failure strength surface, adhesive interfacial fracture energy, as well as the energy release rate for the binding system of the aluminum alloy/epoxy adhesive/aluminum alloy. The obtained results provide a scientific basis for deeply understanding the strength and toughness properties as well as the failure mechanism of the metal adhesive system, and have an important guiding for the optimization design and property evolution of the metal adhesive system. Through present systematic research and analysis, we come to the following conclusions: The tensile failure of the aluminum alloy/epoxy/aluminum alloy adhesive system globally displays the brittle-elastically failure behavior. Failure mode is the fracture along the adhesive interface of adhesive layer. Both failure strength and interfacial fracture energy display the strong size effect when adhesive layer thickness is at hundred micron level. Interfacial adhesive strength increases obviously as adhesive thickness decreases. At critical state the average normal stress and average shear stress are approximately situated at a same circle on the strength failure surface. The interfacial fracture energy decreases obviously as adhesive layer thickness decreases. Both interfacial failure strength and interfacial fracture energy are closely depended on the interfacial adhesive angle.

2017, 49(6): 1213-1222. doi: 10.6052/0459-1879-17-321

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FAST ALGORITHMS FOR DETERMINING POSITIVE DEFINITENESS OF LARGE SCALE MATRICES IN SOLID STRUCTURE ANALYSIS

Xu Hui, Liu Bin

In order to determine the positive definiteness of the super-large-scale matrix in the structural stability analysis, the parallel computing method must be adopted. However, the traditional direct methods such as the eigenvalue’s analysis, the master subordinate determinant’s computation and LDLT decomposition are difficult to realize in parallel computing. In this paper, some iterative algorithms which are suitable for parallel computing are proposed. A new approach is developed that determining the positive definiteness of a matrix can be transformed into an optimization problem, which is solved by various optimization algorithms. The algorithms based on the steepest descent method and the conjugate gradient method are proposed. Considering the sparseness of the stiffness matrix of the mechanical system and the weakly non-positive definite property of at the critical buckling state, we propose a method via calculating the stationary point on a cutting plane to determine the non-positive definite matrices. In order to ensure the accuracy of the determination of strong non-positive definite matrices, a hybrid method combing the cutting plane method and the conjugate gradient method is developed. The numerical results show that the proposed algorithms are accurate and efficient. The conjugate gradient algorithm is more efficient for strongly non-positive definite matrices while the hybrid method is more efficient for the weak non-positive definite matrices. These algorithms are easy to realize in parallel computing on the cluster and can quickly determine the positive definiteness of large-scale matrices.

2017, 49(6): 1223-1230. doi: 10.6052/0459-1879-17-292

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NUMERICAL ANALYZITION OF NANO-PARTICLE FOLLOWING FEATURES FOR RAYLEIGH SCATTERING VELOCITY MEASUREMENT TEST IN LOW DENSITY WIND TUNNEL

Li Zhonghua, Li Zhihui, Chen Aiguo, Wu Junlin

The scattering light intensity can be enhanced in Rayleigh scattering measurement velocity test by adding a small quantity of nano-particles into low density wind tunnel flow field. It is a key factor for the accuracy of measurement result whether nano-particles can adapt the variation of the flow velocity. To investigate the measurement velocity of nano-particle by Rayleigh scattering test whether or not can represent the local flow field velocity, a two-way coupling DSMC method used in rarefied two phase flow is applied to simulate following features of nano-particle in low density flow filed with large grads. TiO₂ particles with 10 nm, 50 nm, 100 nm diameter in low density hypersonic flows around a spaceship model in M6 and M12 cases are carried out respectively. It is shown that the following features of variety size nano-particles in different rarefication flow are distinguishing, and the following feature of smaller size nano-particle is good in complex hypersonic flow. In simulation results, 10 nm nano-particle's following feature in lower rarefication of M6 is better, and good agreement with Rayleigh scattering measurement result. Following features of particle with diameter larger than 50 nm are bad, and in higher rarefication of M12, even 10 nm nano-particle's following feature become worse. This means that velocity of particle measured by Rayleigh scattering can not reflect velocity of flow field.

2017, 49(6): 1243-1251. doi: 10.6052/0459-1879-17-108

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STUDY OF THREE-SHEAR STRESS UNIFIED STRENGTH THEORY

Gao Jiangping, Yang Hua, Jiang Yufei, Wu Pengge, Sun Shijie

The strength theory is an important research subject in advanced mechanics. Many strength theories and important experimental results have been put forward by the scholars all over the world since 200 years ago. Different mathematical expressions were deduced based on different assumptions and mechanical models in these theories which can only be applied to some specific materials. What is the relationship among various strength theories? Can we propose a unified strength theory that adapted to more kinds of materials? Considerable effort has been devoted to this important problem by many scientists all over the world since the end of the 19th century, but it has not been solved. The three-shear stress unified strength theory has been put forward and verified by the method of combining the theoretical study with the experimental verification in this paper. It is considered that the material will failure when the function of the three principal shear stresses and their corresponding three normal stresses which acting on the main shear planes of the dodecahedron element reaches a magnitude. The three-shear stress unified strength theory is the whole force theory, it uses a unified linear expression to contain or approximate the existing and other newly various single and unified, linear and unlinear, convex and non-convex strength theory, it forms a new strength theory system which the inner boundary is the single-shear strength theory and its external boundary is the three-shear stress strength theory, it brings about the highly unity of the strength theory, it develops the unified strength theory which can suitable for different kinds of materials under various stress states from the single-shear strength which only suitable for some specific materials under specific stress states, and it can make full use of the potential strength of the materials. It is shown that the three-shear stress unified strength theory can be widely suitable for different kinds of materials under various stress states from the fact that a large number of experimental results of materials are in agreement with this theory.

2017, 49(6): 1322-1334. doi: 10.6052/0459-1879-17-081

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DYNAMICAL ARTIFICIAL BOUNDARY FOR FLUID MEDIUM IN WAVE MOTION PROBLEMS

Liu Jingbo, Bao Xin, Tan Hui, Wang Jianping, Guo Dong

The wave radiation effect of infinite fluid medium is an important factor affecting the dynamic response of sea area engineering. Artificial boundary is an effective method to realize the numerical analysis of near-field wave motions in such open systems. In this paper, the dynamic artificial boundaries of open domain fluid medium are deduced based on the theory of fluid wave motions in displacement scheme. The dynamic artificial boundary conditions of wave motions in one-dimensional, two-dimensional and three-dimensional fluid media are formed respectively. As a result, the dynamic artificial boundary of plane wave in one-dimensional fluid medium is classical viscous boundary. On the two-dimensional artificial boundary of cylindrical wave and three-dimensional artificial boundary of spherical wave, the nodal stress is proportional to the speed and acceleration of the node. Therefore, the boundary conditions of these two dimensions can be equivalent to the artificial boundaries composed of the damping-mass system. Furthermore, the corresponding numerical simulation techniques of the fluid medium dynamic artificial boundaries proposed in this paper are discussed, and the realization methods on ANSYS platform are given. Examples of the near-field dynamic response problems show that, for the simulation of the transmission and absorption of the axisymmetric and the non-axisymmetric wave motions. in fluid medium, the calculation accuracies of the dynamic artificial boundaries proposed in this paper are relatively high. The reliability and practicality of those artificial boundaries are verified. The artificial boundaries of fluid medium developed in this paper can be combined with large commercial finite element software, which can provide some insight in the dynamic analysis methods of sea area engineering including sea area terrains and islands.

2017, 49(6): 1418-1427. doi: 10.6052/0459-1879-17-199

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LARGE EDDY SIMULATION ON THE EVOLUTION AND THE FAST-TIME PREDICTION OF AIRCRAFT WAKE VORTICES

Lin Mengda, Cui Guixiang, Zhang Zhaoshun, Xu Chunxiao, Huang Weixi

As the commercial air transport increasing in China, the problem of flight delays is increasingly serious. Wake separation (the minimon separation between the leading and following aircraft to avoid wake encounter) limits the capacity of airports. Aimed at this problem, this paper study the evolution of wake vortex with large eddy simulation (LES). The self-adaptive grid method is applied to the LES of wake vortex to improve the computation efficiency and a lift-drag model is applied to the wake vortex generation process to simulate the roll up phase. Based on the LES wake vortex evolution database, a fast-time wake separation prediction system is established. Given the real time ambient wind field and the aircraft parameters, the prediction system can output the suggested wake separation. The results show that under the average wind condition in Beijing Capital International Airport in 2014, the current wake separation can be reduced by 7%~50% with the established system, thus the airport capacity can be considerably improved.

2017, 49(6): 1185-1200. doi: 10.6052/0459-1879-17-198

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FLOW STRUCTURE IN THE TURBULENT BOUNDARY LAYER OVER DIRECTIONAL RIBLETS SURFACES

Cui Guangyao, Pan Chong, Gao Qi, Akira Rinoshika, Wang Jinjun

The statistical characteristics and flow structures for turbulent flow over smooth, convergent and divergent riblets flat plate with zero pressure gradient are investigated with two-dimensional time-resolved particle image velocimetry (TRPIV). It is shown in the wall-normal planes of the convergent and divergent riblets flat plate that, compared to the smooth flat plate, the local boundary layer thickness, wall friction velocity, turbulent fluctuation and Reynolds stress are evidently reduced over the divergent surface. Furthermore, the effect of convergent riblets flat plate on turbulent boundary layer flow is different from the divergent one, which causes the near wall fluid move away and results in an increment of about 43% for turbulent boundary layer thickness. Meanwhile, the large scale coherent structures are more likely to be formed for flow over convergent riblets surface, this is not benefit for drag reduction. Besides, the population of the prograde vortices reaches a maximum value in the log region of turbulent boundary layer, and which appears much closer to the divergent riblets surface than the convergent one. The ejection and sweep induced by the prograde vortices make a great contribution to the mean shear in turbulent boundary layer, and it is the decrease of the prograde vortices which results in the reduction of the wall friction for the diverqent riblets surface.

2017, 49(6): 1201-1212. doi: 10.6052/0459-1879-17-252

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NEW STRUCTURAL DESIGN OF SPHERICAL PRESSURE HULL FOR DEEP-SEA SUBMERSIBLES:A MULTILAYER AND PRESSURE REDISTRIBUTION APPROACH

Zhang Yin, Liu Xiaoming, Lei Xianqi, Sun Chengqi, Fang Xin, Wei Yujie

The pressure hull is the most important key structure to a deep-sea submersible, whose safety and overall performance depend on the integrity of the pressure hull. The current single shell design of the pressure hull is reviewed and a new design based on the multilayer and pressure redistribution mechanism is also proposed in this study. The design is inspired by two deep-sea animals of sperm whale and nautilus. The two mechanisms, the multilayer structure of sperm whale and the shell substructure divided by the septa of nautilus, are synthesized in the design to improve the pressurebearing capacity of the hull. Compared with the one layer structure of the pressure hull, the new design increases both the structural strength and buckling load. Furthermore, the new design can also significantly improve the overall performance of the deep-sea submersible by enlarging the hull volume, enhancing its reliability and lessening the technical challenges of fabricating ultra-thick shell structure. Because the truss structure is introduced in the new shell design, which effectively divides a spherical shell into several substructures of cylindrical shell, a formula is strictly derived to evaluate the truss effect on the buckling load bearing capability of a cylindrical shell. The difference between the newly derived formula and the formula of the Taylor basin, which is summarized from the experimental data and widely used as a standard for the current design of submersible shell, is only 6%. Furthermore, this new derivation also lays a solid theoretical foundation for our new shell design.

2017, 49(6): 1231-1242. doi: 10.6052/0459-1879-17-156

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CHARACTERISTIC OF DROPLET OSCILLATION ON THE SURFACE OF RECTANGULAR HYDROPHOBIC GROOVES

Dong Qiqi, Hu Haibao, Chen Libin, Yu Sixiao

Droplet oscillation is an important phenomenon in nature, it has important scientific research value. Since the liquid droplet behavior when impinging on the hydrophobic plate surface with grooved texture is obviously different from that on the smooth plate surface, the characteristics of the oscillation of the height and the contact line of water droplet on the rectangular hydrophobic grooves are studied via high-speed camera. Due to the anisotropic wetting of the rectangular hydrophobic grooves, the length of the contact line of water droplet in the parallel direction of the groove is longer than that in the vertical direction. However, it does not affect the period of the attenuation oscillation in the height direction, which means the droplet oscillation period has no relationship with the width of the slot. What's more, due to the binding effect of the barrier on the surface within hydrophobic grooves, the spreading and retraction of the contact line do not follow the typical damping oscillation law. It stabilizes rapidly after several oscillations. For example, when the velocity of water droplet is 0.61 m/s, the contact line is stable after 2 oscillations, but the water droplet is still oscillating. In addition, we give the reason why the water droplet oscillation period is irrelevant to the groove size.

2017, 49(6): 1252-1259. doi: 10.6052/0459-1879-17-225

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EXPERIMENTAL INVESTIGATION ON THE EVOLUTION OF INTERNAL SOLITARY WAVE OVER A RIDGE AND ITS ACTING FORCES ON A SUBMERGED SLENDER BODY

Gu Mengmeng, Wei Gang, Deng Bing, Du Hui, Wu Junlin

The configuration of internal solitary wave (ISW) over a ridge terrain will largely increase the uncertain factors threatening the safety for marine architecture and submerged vehicle. Laboratory experiments are conducted to examine an ISW propagating over a ridge terrain and its interaction with a submerged slender body in a large-type gravity stratified fluid tank. The evolution characteristics of the ISW is measured by using multi-channel conductivity-probe arrays and dyeing identification method, and its action on the body exerted by the ISW is measured by a set of three-component force sensor. The experimental results have shown that when an ISW of depress propagates over a ridge terrain its wave configuration will be changed significantly, including that its amplitude will increase on the windward side of ridge, its lee side will be up at the top of ridge and its wavelength will be longer on the leeward side of ridge. Furthermore the configuration change of the ISW will affect obviously the characteristics of the action on a slender body, including that the downward force becomes larger distinctly on the windward side of ridge, the upward force is more significant at the top of ridge and the effective time of the action on the body becomes longer at the leeward side of ridge. Therefore, the body movement trend can be judged roughly based on the force behaviors, i.e. the largest sinking will happen on the windward side of ridge and the stronger surging towards the direction of ridge will do on the windward side of ridge.

2017, 49(6): 1260-1271. doi: 10.6052/0459-1879-16-322

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A STUDY ON DROPLET VELOCITY OF ETHANOL DURING ELECTROSPRAYING PROCESS AT CONE-JET MODE

Gan Yunhua, Jiang Zhengwei, Li Haige

An analysis on the velocity characteristics of droplets generated from electrospraying is the key to understand the formation and evolution of the spray shape. Combining with the experimental results of ethanol electrospraying at cone-jet mode, a two-dimensional axisymmetric model of electrospraying was established. Based on the droplet motion equations, air motion equations, electric field equations and user-defined functions, the model was numerically solved to obtain the spray morphology, the space electric field distribution and the droplet velocity field distribution at cone-jet mode. The effect of air inlet velocity on the spray shape and velocity field distribution of ethanol/air coaxial jet was also discussed. The results indicate that the air flow field has a strong interaction with the droplets at the periphery of the spray, leading to a smooth variation of the droplet velocity distribution near the axis of the spray, while the droplet velocity distribution at the periphery of the spray varies drastically along the radial direction. As the coaxial air inlet velocity increases, the spray shape tends to diverge first. But when the air inlet velocity increases to be greater than the axial velocity of the spray droplets, the spray shape tends to gather. Therefore, in addition to changing the applied voltage, liquid flow rate or electrode pattern, controlling the air inlet velocity to affect the spray velocity field can be an efficient way to control the electrospraying.

2017, 49(6): 1272-1279. doi: 10.6052/0459-1879-17-226

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INSTABILITY OF COUPLED THERMO-SOLUTE CAPILLARY CONVECTION IN LIQUID BRIDGE AND CONTROL BY ROTATING MAGNETIC FIELD

Zou Yong, Zhu Guiping, Li Lai, Huang Hulin

Floating zone method is an important technology for growth of high-integrity and high-uniformity single crystal materials due to its free of crucible contamination. However, the capillary convection in the melt brings a great challenge to the floating zone crystal growth. This is because the instability of convection will cause the formation of some crystal defects such as microscopic imperfections and macroscopic stripes. Therefore, it is very important to investigate the behaviors of the capillary flow and control its instability in order to improve the quality of the produced single crystal materials. In this paper, numerical simulations are performed to investigate all kind of the capillary convection in the half floating liquid bridge on the Si_xGe_1-x system. And the impact of the external rotating magnetic field is also investigated on the stability of capillary convection. The results show that the purely solute capillary convection is a two-dimensional axisymmetric model, and the temperature field is mainly determined by thermal diffusion while the concentration field is dominated by convection and solute diffusion together. On the other hand, the purely thermo-capillary convection presents three-dimensional unsteady axisymmetric flow. The concentration distribution is closely related to the flow direction of thermo-capillary convection. The isotherms bend in the region with strong convection. The coupled solute and thermocapillary convection is a three-dimensional periodic rotating oscillatory flow. When the rotating magnetic field is applied, the circumferential velocity of the melt increases with increasing radius. Both the concentration field and the flow field in the melt show a two-dimensional axisymmetric distribution.

2017, 49(6): 1280-1289. doi: 10.6052/0459-1879-17-102

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A NEW INTERFACE CAPTURING METHOD BASED ON DOUBLE INTERFACE FUNCTIONS

Li Kang, Liu Na, He Zhiwei, Luo Longshan, Tian Baolin

We describe a novel double-interface-function (DIF) reconstruction method for efficient numerical resolution of a compressible two-phase flow. Based on the new method, double sine interface capturing scheme (DSINC) is obtained. Five-equation model is solved to analyze the effect of different interface functions such as DIF and Single Interface function (SIF) on the interfaces captured numerically. Near the interfaces, the algorithm uses the DIF or SIF as a basis for the reconstruction of a sub-grid discontinuity of volume fractions. In regions away from the interfaces, WENO is used to reconstruct the convective term, and time integration of the algorithm is done by employing the TVD Runge-Kutta method. Comparing with tangent of hyperbola for interface capturing (THINC) using SIF method, the left and right states reconstructed by DSINC is simpler and we need not solve a transcendental equation. Numerical results are shown with the Mie-Grüneisen equation of state (EOS) for sample problems such as discontinuous advection, two-phase triple problem and shock-bubble interaction problem with THINC and DSINC. It can be found that DSINC is able to get as efficient resolution interface as THINC and shows to be more stable in the simulation.

2017, 49(6): 1290-1300. doi: 10.6052/0459-1879-17-210

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ENERGY DISSIPATION IN TAPPING MODE ATOMIC FORCE MICROSCOPY

Wei Zheng, Sun Yan, Wang Zairan, Wang Kejian, Xu Xianghong

There are many imaging modes in atomic force microscopy (AFM), in which the tapping mode is one of the most commonly used scanning methods. Tapping mode can provide height and phase topographies of the sample surface, in which phase topography reflects more valuable information of sample surface, such as surface energy, elasticity, hydrophilic hydrophobic properties and so on. According to the theory of vibration mechanics, the phase is related to the energy dissipation of the vibration system. The dissipation energy between the tip and sample in tapping mode of AFM is a very critical key to understanding the image mechanism. It is affected by sample properties and lab environment. The loading and unloading curves of tip and sample interaction are given based on the JKR model while the capillary force is not considered. The unstable position of jump out between the tip and sample is show, and then the energy dissipation in a complete contact and separate process is calculated. The effect of roughness of sample surfaces on energy dissipation is also discussed. It is provided that the extrusion effect is the dominant fact or in liquid bridge formation by characteristic time contrast when capillary force is considered in tapping mode AFM. The effects of relative humidity on energy dissipation are numerically calculated under isometric conditions. Finally, the relationship between phase image of AFM and sample surface energy, Young's modulus, surface roughness and relative humidity is briefly explained by one-dimensional oscillator model. The analyses show that the difference of surface roughness and ambient humidity can cause phase change, and then they are considered as the cause of artifact images.

2017, 49(6): 1301-1311. doi: 10.6052/0459-1879-17-223

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CRACK INTERACTING WITH AN INDIVIDUAL INCLUSION BY THE FRACTURE CRITERION OF CONFIGURATIONAL FORCE

Gu Bin, Guo Yuli, Li Qun

Based on the concept of configurational force, a new fracture criterion is proposed to determine the crack initiation and the direction of crack propagation. The criterion assumes that when the resultant configurational force reaches a critical value, the crack begins to grow, while the direction of the crack propagation is the vector direction of the resultant configurational force. Moreover, the finite element method of configurational force is developed to realize the numerical simulation of crack propagation. The crack propagation problem of the structure with an individual hole/inclusion in engineering is studied. The results show that the crack propagation criterion based on configurational force can predict the crack growth interacting with an individual hole/inclusion well, the results of the numerical simulation are consistent with experimental results, which verifies the validity of the simulation method of the crack propagation. The numerical simulation of the interference between cracks and inclusions (holes, soft inclusions or hard inclusions) shows that the inclusion near tip of the crack has an important influence on the propagation of the crack. The propagation direction of the crack is related to the relative position of crack and inclusion, and the type of inclusion. The soft inclusion and the circular hole attract the crack to expand, while the hard inclusion will repel the crack growth, and the crack will bypass the hard inclusion during the propagation. When the intersection angle of the crack and inclusion is small, the effect of inclusion on crack propagation is obvious. The inclusion has little effect on crack propagation when the angle is large. Particularly, when the angle is 45°, and the growth of soft inclusion may suppress the crack propagation. This study can help to understand the crack propagation in the structure with voids and inclusions, and have important guiding significance for the fracture problems in engineering.

2017, 49(6): 1312-1321. doi: 10.6052/0459-1879-17-209

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CRACK FACE CONTACT PROBLEM ANALYSIS USING THE SCALED BOUNDARY FINITE ELEMENT METHOD

Zhang Peng, Du Chengbin, Jiang Shouyan

In the case of arbitrary tractions on the side faces of the crack, a polynomial function of the radial coordinate can be employed to describe the side face loads in the scaled boundary finite element method (SBFEM). The SBFEM new shape function considering the side face loads is presented. The corresponding stiffness matrix and equivalent node load is derived together based on the SBFEM new shape function. The model of crack face contact using the SBFEM is proposed in this paper for the first time. Lagrange's multiplier method is used to establish the contact constraints of contact model between crack faces. The governing equations for the nonlinear surface contact problems in SBFEM is derived, including adhesion contact problems and sliding friction problems. The elements where the crack faces lie are divided into non crack tip elements and the crack tip element. For the former, the crack faces act as the boundary of the SBFEM element, the contact tractions on the boundary can be assigned to the nodes equivalently and the Lagrange's multiplier is applied for the point constraints. For the latter, the interpolation field of Lagrange's multiplier is constructed on the whole side faces. The Lagrange's multiplier is assumed to be linear along the side faces, the segment constraint approach is proposed to optimize the fulfilment of the contact constraints along the crack faces.By comparing the results of the calculation of analytical solution and software ABAQUS on three different numerical contact problems of crack faces, the accuracy and effectiveness of the proposed point-to-point and segment-to-segment contact model for fracture surfaces contact problems is verified in this paper.

2017, 49(6): 1335-1347. doi: 10.6052/0459-1879-17-195

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APPROXIMATE THEORY AND ANALYTICAL SOLUTION FOR DYNAMIC CALCULATION OF VISCOELASTIC LAYERED PERIODIC PLATE

Xu Sihui, Wang Binglong, Zhou Shunhua, Yang Xinwen, Li Yaochen

Rail transit loading and viscoelastic of material are mostly ignored in the previous dynamic calculations of the periodic vibration isolation structures. Approximate theory and analytical solution for viscoelastic layered periodic plate subjected to vertical moving harmonic loading is established, and the viscoelastic of material and the transverse shear deformation are considered. In this theory, Reissner-Mindlin assumption and additional equation of shear deformation are introduced, and the relation between the normal rotation and the shear stress of neutral plane is obtained on the assumption that the transverse shear deformation of the plate's neutral plane is the overall shear deformation of the cross section. Vibration governing equation of viscoelastic layered periodic plate is proposed according to equilibrium equations and stress continuity conditions, and vertical displacement in Fourier series is derived as well. The model is validated by the good agreement with solution of the classical laminate model and the finite element method (FEM).The results show that:(1) Vibration response at the natural frequency of plate can be significantly reduced by substituting viscoelastic layered periodic plate for homogeneous one, but vibration amplification in local low frequency band is aroused as well. (2) The vertical displacement of the plate increases with the increment of the loading velocity, and increase trend slows down once velocity above 300 km/h. (3) Shear modulus of viscoelastic layer can be designed to achieve the optimal vibration isolation characteristic. (4) Vibration response is not susceptible to damping characteristic in low frequency band. (5) It's appropriate to increase the plate length, within the engineering requirement, to improve the vibration isolation performance.

2017, 49(6): 1348-1359. doi: 10.6052/0459-1879-17-248

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ANALYSIS OF GROUND VIBRATION CONTROL BY GRADED WAVE IMPEDING BLOCK

Ma Qiang, Zhou Fengxi, Liu Jie

Wave impeding block (WIB) vibration isolation system as an effective measure for vibration pollution control is applied in practical engineering gradually, but the previous studies mostly focused on the single-phase solid homogenous materials, few research have been on the vibration isolation performance of wave impeding block with materials properties that have a continuous variation along space relatively. Based on the functionally graded material, a new type of foundation vibration isolation system is proposed. Considering setting the graded wave impeding block in the elastic foundation which subjected to surface strip harmonic load, using the Fourier transform and Helmholtz vector decomposition, the calculation formula of reverberation ray matrix method (RRMM) is established for two-dimensional transient response of elastic foundation based on the line elastic theory. Assuming that the material properties of graded wave impeding block have an exponential law distribution along the thickness-coordinate, by using numerical inverse Fourier transformation, the displacement and the stress are obtained. Via numerical examples, the effectiveness of vibration isolation of graded wave impeding block is compared to conventional single phase solid homogenous wave impeding block, and the influences of physical and mechanical parameters including the gradient factor, the depth and the thickness of graded wave impeding block are analyzed. The results show that the graded wave impeding block can effectively reduce the vibration amplitude, and compared with the single phase solid homogenous wave impeding block isolation system, graded wave impeding block isolation system has better effect. The amplitude of displacement and stress is decreased with the increase of gradient factor. The effect of vibration isolation of graded wave impeding block improved with the increased of the thickness, but reduced with the increasing of the embedded depths.

2017, 49(6): 1360-1369. doi: 10.6052/0459-1879-17-221

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RESEARCH ON MODELING AND NUMERICAL METHOD OF FREE STANDING BODY ON PLANAR RIGID MULTIBODY DYNAMICS

Zhang Runsen, Wang Qi

A multibody system composed of free standing body and the basic platform is investigated by non-smooth dynamics of multibody system. Dynamic equations and numerical method of the system with non-smooth contacts are proposed. The free standing body consists of main body and supporting legs, which are connected by revolute joints with viscoelastic moments. The contact forces between free standing body and the basic platform are simplified as normal forces and frictional forces of contact points. Moreover, the modified Hertz contact model and Coulomb's law for dry friction are employed to describe normal forces and frictional forces, respectively. And the configuration coordinates of Cartesian coordinate system are used as the generalized coordinates. Firstly, the system's dynamic equations are established by Lagrange's equations of the first kind and the motion of basic platform is regarded as a rheonomous constraint. The problem of constraints violations is solved by Baumgarte stabilization method. Secondly, the numerical method of the multibody system are proposed, which is based on the event-driven schemes and linear complementarity formulations. The complementary formulations of friction saturations and the relative accelerations in the tangential are given, while the relative velocities in the tangential of the contact points are equal to zero. Therefore the judgements of stick-slip transitions for contact points and the solutions of frictional forces in stick situation could be solved as a linear complementarity problem. And the linear complementarity problem is solved by Lemke's algorithm. Finally, an appropriate step is chosen by the simulation. Then the numerical simulations denote the stick-slip phenomenon and the influence of basic platform as well as mass centre's position.

2017, 49(6): 1370-1379. doi: 10.6052/0459-1879-17-235

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COMPLEX RELAXATION OSCILLATION TRIGGERED BY BOUNDARY CRISIS IN THE DISCRETE DUFFING MAP

Chen Zhenyang, Han Xiujing, Bi Qinsheng

Multiple-time scale problems are ubiquitous in both science and engineering, while the slow varying parameter is one of the iconic feature of multiple-time scale. However, up till now, most of bifurcation structures and oscillation patterns revealed by literatures are relatively simplex. In this paper, we take the non-autonomous Duffing map as a example to explore family of complex relaxation oscillation patterns, which are little concerned by previous study. The fast subsystem exhibits an S-shaped fixed point curve, and the stable upper and lower branches evolve into chaos by a cascade of Flip bifurcations. What's more, we can observe a pair of critical parameter values under some parameter conditions, which lead to the catastrophe vanish of chaotic attractors. When the bifurcation parameter reaches these values, chaotic attractors may contact with the unstable fixed point or just stay in a distance apart. By simulating the distribution of basins of attraction owned by fast subsystem, we show that there exist critical points of boundary crisis, nearby which chaotic attractor evolved from stable fixed points can coexist with period-2ⁿ (n=0, 1, 2, …) attractor or even another chaotic attractor. When the non-autonomous term (i.e., the slow variable) passes through critical points, distruction of bi-stability may lead to the transition from chaotic attractor in pre-crisis stage to the coexisting attractor, thus the boundary crisis motivates different patterns of symmetric relaxation oscillation. In particular, patterns here show structures containing different number of delay flip bifurcations, owe to the fact that delay quantities of Flip points in different level take disparate magnitude. Our results enrich dynamical mechanisms of multiple-time scale in discrete systems.

2017, 49(6): 1380-1389. doi: 10.6052/0459-1879-17-138

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AN EFFICIENT DYNAMIC MODELING METHOD OF AN AXIALLY MOVING CANTILEVER BEAM AND FREQUENCY RESPONSE ANALYSIS

Hua Hongliang, Liao Zhenqiang, Zhang Xiangyan

The dynamics of the axially moving beam has wide application in engineering, such as robot manipulators, machine tools and gun barrel, et al. Computing the dynamic response of axially moving beam is an important method to evaluate the dynamic performance and finally the structure design. The time-varying motion equations of the axially moving cantilever beam are derived using the Rayleigh-Ritz method and Lagrange's equation. The power series function is used to construct the trial function to solve the dynamic problem. Due to the good integral and differential performance of power series function, the derivation is easy to be carried out in the form of matrix. In this way, the symbolic computation software can generate the MATLAB program directly. And the generated MATLAB program can be used to conduct the dynamic computation with few modifications, because the basic data unit of MATLAB is matrix. The overall process is efficiency and the time from dynamic modeling to computation is greatly reduced. Through four sets of numerical examples, the computational accuracy of the presented method is validated by comparing the dynamic responses with those from previous literatures. Then, the effects of fitting order of the power series function on computational accuracy are discussed. And the principle to select the fitting order of the power series function to achieve good convergence and computational accuracy is given. Based on the dynamic model, the effects of axial motion frequency on transverse vibration are studied. The effects of axial vibration amplitude on the frequency response characteristic are explored. And the difference between considering gravity and neglecting gravity effect are compared.

2017, 49(6): 1390-1398. doi: 10.6052/0459-1879-17-182

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RESEARCH ON DYNAMIC MECHANICAL RESPONSE AND CONSTITUTIVE MODEL OF PORCINE LIVER

Wang Baozhen, Hu Shisheng

Impact-induced injuries to the abdominal organs appear frequently in traffic accidents and even cause serious life-threatening. The liver is one of the most vulnerable abdominal organs, leading to high mortality rate. An understanding of the dynamic mechanical behaviors of the liver could aid in the design of the safety equipment to effectively reduce the occurrence of liver injury. The specimens of liver parenchyma were harvested from the fresh porcine livers. The Instron material testing machine was used to obtain the quasi-static responses up to the point of failure at the two strain rates (0.004 s^-1 and 0.04 s^-1) and two loading directions (perpendicular and parallel directions to the liver surface). The high strain rate (1 300 s^-1, 2 400 s^-1, 4 500 s^-1) experiments were performed using the modified SHPB equipment along the liver surface. The results show that all stress-strain curves are nonlinear and concave upward. Stress level of curves is very low at the initial stage up to about 30% strain, and then increases steeply. No significant differences in the failure stress (about 0.45 MPa) and strain (about 48%) were observed for two loading rates and directions at quasi-static tests. However, it was found that the liver tissue became much stiffer at high strain rates than at quasi-static rates, indicating the strain rate dependence. The Yeoh hyperelastic material model was used to characterize the mechanical behaviors of the liver at quasi-static loading. Based on an improved visco-hyperelastic model, a rate-dependent constitutive model was proposed to describe the responses of the liver from the low strain rates to high strain rates. The model is found to be in excellent agreement with the experimental results.

2017, 49(6): 1399-1408. doi: 10.6052/0459-1879-17-238

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OPTIMIZATION DESIGN OF DEGRADABLE POLYMER VASCULAR STENT STRUCTURE

Zhao Danyang, Liu Tao, Li Hongxia, Wang Minjie

Due to the low stiffness of polymers, polymeric stent has lower radial support capability compared to metallic stent. Therefore, the width and thickness of the stent are usually increased to improve its radial support capability, which can not only reduce the flexible performance of the stent and the area of the vascular lumen, but also increase the surface coverage and thus increase the risk of in-stent restenosis. In order to design polymeric stent with smaller strut width and thickness and improve its radial support capability, an optimization method combining with Kriging surrogate model and finite element method was used to optimize the geometries of stent. Kriging surrogate model was used to construct the approximate function relationship between design objectives and design variables. Optimized Latin Hypercube Sampling method was used to select the initial sample points. EI function was used to balance global and local search and tend to find the global optimal solution. As an example, ART18Z polymeric stent was studied in this paper. Firstly, the strut width and thickness of the stent were respectively reduced by 0.02 mm, and then the optimization method was used to optimize the key geometric parameters of ART18Z stent. The numerical results show that the overall service performance of ART18Z stent was improved after optimization and the proposed optimization method can be effectively applied to the optimal design of the polymeric stent.

2017, 49(6): 1409-1417. doi: 10.6052/0459-1879-17-214

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REVIEW OF THE TENTH NATIONAL SYMPOSIUM ON FLUID MECHANICS FOR YOUNG SCHOLARS

Huang Zhangfeng, Zhang Panfeng, Zhan Shige

The paper briefly introduced the twenty years' history of the National Symposium on Fluid Mechanics for Young Scholars, and focused on the tenth National Symposium on Fluid Mechanics for Young Scholars. Reports of the symposium were reviewed and some constructive comments and suggestions were put forward.

2017, 49(6): 1428-1434. doi: 10.6052/0459-1879-17-313

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2017 Vol. 49, No. 6

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