力学学报

DEVELOPMENT STATUS, TREND AND THE PROBLEMS OF MECHANICS OF TIDAL CURRENT ENERGY

Zhang Li, Li Zhichuan

As energy and climate change are currently two of the most important issues in society, many governments in the world are paying more attentions to renewable energy. Tidal current energy is a kind of ocean renewable energy; its resources are rich and its development prospects are very good. Since the 21st century, the development of tidal current energy has made great progress worldwide; a variety of tidal current energy generating devices has been in stage of demonstration project or stage of pre-commercialization. In this aspect, people are faced with the key mechanical problems of how to use all kinds of conversion devices to improve the conversion efficiency of tidal current energy. The situation of tidal current energy resources in China, the latest status of development and utilization at home and abroad, key technologies for tidal current energy utilization and utilization prospect of tidal current energy have been reviewed. Finally, the suggestion of technological development has been given combining with the present situation in China. The main contents of this paper are as follows:First, it is about the generation, characteristics and distribution of tidal current energy. The generation of tidal current, the characteristics of tidal current energy and the distribution of tidal current energy resources are mainly introduced in this part. Second, it's the development status of the technologies of tidal current energy. The process of the technologies for tidal current energy utilization and the development status in China and abroad are introduced. Third, the key technologies for tidal current energy utilization are described, including the capture and conversion of energy, transmission systems and turbines, array layout of tidal current energy conversion, construction of offshore power grid, support structures, etc. Fourth, it is the prospect of development and utilization of tidal current energy. The research focus of tidal current energy technologies at home and abroad are pointed out. Finally, the suggestions and prospects for the development and utilization of tidal current energy in China are given.

2016, 48(5): 1019-1032. doi: 10.6052/0459-1879-15-299

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TRPIV EXPERIMENTAL INVESTIGATION OF THE EFFECT OF RETROGRADE VORTEX ON DRAG-REDUCTION MECHANISM OVER SUPERHYDROPHOBIC SURFACES

Su Jian, Tian Haiping, Jiang Nan

The discovery of coherent structures in turbulent in the last century suggests affinew direction for turbulent controy, especially the vortex in the near-wall region, which has a great contribution to the skin friction. In this study, the spanwise vortex characteristics, compared between superhydrophobic (SH) surfaces and hydrophilic (PH) surfaces in the turbulent boundary layer, were investigated by time-resolved particle image velocimetry (TRPIV). Firstly, the multi-scale spatial locally-averaged vortices were utilized to extract the spatial topologies of the spanwise vortex head (clockwise vortex) and retrograde vortex, and this method accurately identified the vortex core and excluded the interference of the minor scales vortex. Secondly, the distributions of streamline around clockwise and retrograde vortex visualized vortex structure properly to study relative position relation between the two kinds of vortex. Finally, through the comparative research on the number of retrograde vortex, for SH surfaces, the occurrence probabilities of retrograde vortex seems to be bigger than SH surfaces. There is a conclusion that retrograde vortex can inhibit the development of the corresponding clockwise vortex and restrain its strong ejection and sweep events. Accelerating the fluid in the near-wall region is also the direct cause for the drag-reduction effect of SH surfaces. These show that the drag-reduction effect (approximately 5.8% when Re_δ≈13 500) of SH surfaces is related to the differences of retrograde vortex.

2016, 48(5): 1033-1039. doi: 10.6052/0459-1879-16-140

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EXPERIMENTAL INVESTIGATION ON FLOWFIELD AROUND BLUNT BODY WITH FORWARD-FACING JET AND SPIKE

Zhang Jiang, Wu Junfei, Ni Wenbin, Ma H, ong

The characteristics of the flow around a blunt body with the combination of forward-facing jet and spike are investigated through wind tunnel experiments, which include the mechanism of steady mode and unsteady mode. The dynamic-force measurement, the dynamic-pressure measurement and the schlieren photograph are involved. The results indicate that there are the steady mode and the unsteady mode for the flow field around the blunt body with the combination of forward-facing jet and spike. The flow is steady as the pressure ratio of the supersonic jet is higher than the critical pressure ratio, while it is unsteady as the pressure ratio of the supersonic jet is lower than the critical pressure ratio. The drag of the blunt body decreases with the increasing of the length of the spike until the length of the spike reaches a certain value. With the enhancement of jet pressure ratio the strength of the reattachment shock waves is weakened significantly, which is beneficial to the eliminating of the hot spot on the shoulder of the blunt body. The pressure on the surface surrounded by the reattachment shock waves is fluctuating intensively under the unsteady mode, which is induced by the self-excited oscillations of shock waves around the blunt body. The dominant frequency of the self-excited oscillation decreases with the increasing of the jet pressure ratio. The mechanism of self-excited oscillation is that the ambient pressure around the jet exit cannot be balanced persistently when the jet pressure ratio is lower than the critical pressure ratio.

2016, 48(5): 1040-1048. doi: 10.6052/0459-1879-16-020

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NUMERICAL INVESTIGATION OF NOISE OF A HIGH SUBSONIC TURBULENT JET

Feng Feng, Guo Li, Wang Qiang

To meet the regulations of aviation noise, noise control of jet engine has grown to become a major issue in aeroacoustics, therefore prediction of jet noise and unfolding its generation mechanism would lay a solid foundation for the noise control. Turbulence evolution and noise of a Mach 0.9 high subsonic jet are investigated by high-order accurate parallel LES (large eddy simulation). Firstly, the fidelity of turbulence result computed by LES is rigorously verified, and the evolution of multi-scale vortex structures is carefully analyzed. Secondly, based on the acoustic source in near field of the jet, the penetrable FW-H (Ffowcs Williams and Hawkings) wave extrapolation method is used to solve the farfield acoustic and analyze the behavior of the dominant modes. Finally, via analyzing mechanism of acoustic source and separating the acoustic modes, the role of the large-scale coherent vortex evolution in the end of potential core play in dominant acoustic modes generation as a form of low wave number wavepackets is investigated. Numerical results show that LES combined with the penetrable FW-H method is able to accurately predict the flow and acoustic features of the high subsonic jet. Furthermore, numerical analysis reveals that the large-scale coherent structure generated by the vortex ring pairing is merging along the jet centerline, which producing the primary acoustic modes dominated at the low azimuth direction and forming a superdirective acoustic field. The azimuth angle of the peak intensity is near to 30°.

2016, 48(5): 1049-1060. doi: 10.6052/0459-1879-15-403

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SHEAR CELL TEST ON TRANSITION OF SHEAR FLOWSTATES OF GRANULAR MATERIALS

Ji Shunying, Sun Shanshan, Chen Xiaodong

The shear flow behaviors of granular materials exist widely in the natural disasters (such as landslide and debris flow) and the industrial process (such as transportation and pumping of mineralmaterials). Granular materials perform various shear flow states under different volume fractions, shear rates and constraint stresses. The investigation of mechanical characteristics in a shear flow process provides an insight to the mechanism of phase transition of granular materials. In this study, a medium-size annular shear cell was developed to study the shear flow states of granular materials and their transition. The shear stress and the volume dilation rate were measured under various normal stresses and shear rates. The experimental results show that the shear stress and the volume dilation rate increase with increasing shear rate. Both of them increase with the square of shear rate piecewise linearly. The inflection points in the linear relations of the square of shear rate versus the shear stress and the volume dilation rate were obtained at the critical shear rate respectively. With the analysis of effective friction coefficis under various shear rates and inertia numbers, the phase transition process between the slow flow and the rapid flow was discussed. The phase transition occurs at the critical shear rate. Moreover, the shear flow states of granular materials were measured under various normal stresses. The critical shear rate decreases with increasing normal stress. This indicates that the normal stress can boost the phase transition between the slow flow state and the rapid flow state. In rapid shear flow state, the effective friction coefficient is independent of the normal stress. The mechanism of phase transition can be well studied with the experiments of shearing granular under various shear rates and normal stresses.

2016, 48(5): 1061-1072. doi: 10.6052/0459-1879-16-049

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EXPERIMENTAL INVESTIGATION OF MIXING RATE IN R-M INSTABILITY OF DIFFUSE GAS CYLINDER INTERFACE

Huang Xilong, Liao Shenfei, Zou Liyong, Liu Jinhong, Cao Renyi

Richtmyer-Meshkov (R-M) instability has attracted extensive attention in many engineering application fields. Shock tube experiment is a widely used technique in the study of R-M instability. Thanks to the molecular-level traceability, planar laser-induced fluorescence (PLIF) diagnostic technique o ers concentration (mole fraction) map of interface gas with high resolution. It shows the way to study the mixing in the instability evolution. Di use gas cylinder interfaces are accelerated by a weak shock wave (Ma=1:25) in the experiment. Using PLIF, the mixing of interface is investigated, which is induced by R-M instability. By changing the aspect ratio of elliptic cylinder, concentration maps of diffuse gas cylinders with three types of initial configurations are obtained. The simple stretching, the secondary instability and the jet caused by extrusion in the concentration field are clearly revealed. Moreover, the mixing rate of different stages of evolution is calculated from concentration field. Attempting to understand the mechanism of mixing, instantaneous mixing rate, total mixing rate of the interface and the probability density distribution of mixing rate are analyzed in detail. At early time, baroclinic vorticity accelerates the mixing through stretching interface and intensifying concentration gradient. As the evolution develops, the secondary instability appears, causing the flow transitions to turbulence as a result of smallscale convection. At meantime, molecular mixing induced by concentration gradient is weakened. There is a competitory relationship between diffusion caused by concentration gradient and convection caused by secondary instability, which control the mixing together.

2016, 48(5): 1073-1079. doi: 10.6052/0459-1879-16-108

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STUDY ON IRRADIATION DAMAGE AND MECHANICAL PROPERTY OF GRAPHENE

Hua Jun, Hou Yan, Duan Zhirong, He Yu

Processing and doping are important methods in the engineering application and development of graphene. Ion irradiation technology is an important approach to realize the processing and doping. The molecular dynamics model of graphene irradiated by Silicon neutral and the tensile model of defective graphene after irradiation damage are established. The defect types and quantities in graphene under different irradiation conditions, including ion dose, energy and angle, are analyzed and the tensile behaviors of defective graphene caused by different incident numbers of Si ions are also investigated. The conclusions are as follows:When the ion energy is small, incident particles will be adsorbed on the surface of graphene; with the increase of ion energy, incident particles can penetrate the target and form some defects; when the ion energy reaches a certain large value, there is no adsorbed atom. With the increase of the ion dose, the numbers of sputtering atoms and defects increase and the main defect is vacancy. The tensile mechanical properties of the corresponding defective graphene, such as tensile strength and limit strain, reduced with the increase of the defects number. The tensile failure mechanisms of the defective graphene caused by irradiation and the pristine graphene are different. The strengthened stage in the tensile curve of the former is shorter and the location of fracture initiation and the fault strike are dominated by the defect cluster.

2016, 48(5): 1080-1087. doi: 10.6052/0459-1879-16-015

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INFLUENCE OF COHESIVE ZONE MODELS SHAPE ON ADHESIVELY BONDED JOINTS

Zhang Jun, Jia Hong

Cohesive zone models have been increasingly used to simulate fracture of adhesively bonded joint. In order to understand the relation between the delamination of the different types of adhesives and the shape of cohesive zone models (CZMs), the uniaxial tension and shear experiments were conducted using two distinct adhesives, an epoxy-based adhesive in a brittle manner and VHB^TM tape adhesive in a ductile manner. Three types of CZMs shapes are adopted, including exponential, bilinear, and trapezoidal models. The results demonstrate that the bilinear CZM more suitably simulate the tension and shear failure of the brittle adhesive, while the exponential CZM suitably describes the ductile adhesive. The cohesive strength, work of separation and the shape parameters are the significant effect factors on the simulation results of the uniaxial tension and shear debonding procedures. Nevertheless, the shape of CZM has certain influences on the simulation of the double cantilever beam fracture. The comparison between the numerical and the experiment results demonstrate that the bilinear CZM more suitably simulate the double cantilever beam fracture of the brittle adhesive, while the trapezoidal CZM suitably describes the ductile adhesive. The investigation results are significant to use CZMs to precisely analyze adhesively bonded joints fracture.

2016, 48(5): 1088-1095. doi: 10.6052/0459-1879-16-064

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STUDY ON HIGHER-ORDER SHEAR DEFORMATION THEORIES OF THICK-PLATE

Duan Tiecheng, Li Luxian

It is still necessary to study the thick plate theory and higher-order shear deformation models with a lot of published work. Starting with the definition of average rotation and the free shear stress condition at the bottom and top surfaces, the displacements on the neutral plane are suggested with a unified higher-order shear deformation model, and then expressed in the orthogonal form. On this basis, the generalized stresses are defined, then the generalized strains are obtained in light of the work conjugate, and the constitutive relations are established for the plate theory. The objectivity of the principle of virtual work in the plate theory is proved for different definitions of rotation, as well as the identity to three-dimensional elasticity theory. Based on the principle of virtual work, the variationally consistent higherorder plate theory and the variationally asymptotic lower-order plate theory are respectively established by deriving the corresponding equilibrium equations and boundary conditions, and then compared with the existing plate theories. The current work originally presents the equilibrium equations of the plate theory in terms of the generalized stresses, and clarifies some fundamental problems such as the relations of different definitions of rotation, the relation between the higher-order plate theory and the lower-order plate theory, and the evaluation of the shear factor. The current plate theory is finally validated by solving the Saint-Venant torsion problem.

2016, 48(5): 1096-1113. doi: 10.6052/0459-1879-16-120

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INFLUENCE OF SURFACE ROUGHNESS ORIENTATIONS ON FRICTION COEFFICIENT OF WHEEL/RAIL SPECIMEN IN OIL LUBRICATION

Cai Baochun, Jiang Huazhen, Wang Wenzhong, Li Zhengyang, Wang Baoan, Yang Bing, Ren Zhiyuan

Adhesion is one of the key factors to maintain safety and stability of train running. Maximum adhesion is related to the friction. The decline of friction results in decrease of adhesion. In fact the friction coefficient mixed lubrication is not only greatly influenced by surface roughness, but also by roughness orientations. However, the previous investigations regarding the effect of roughness orientation on friction coefficient seem to be contradictory. In this paper,the three typical surface roughness orientations, i.e., longitudinal, transverse and rhombus were treated by laser discrete modification technology. The behavior of three patterns of roughness orientations under mixed lubrication were compared to those of without laser treatment. A numerical analysis based on deterministic model with unified Reynolds equation was adopted. Tribology tests with scaled wheel/rail specimens were carried out. It is concluded that the wheel surface with laser patterns greatly enhanced the friction coefficient comparing with the surface without laser pattern. The friction coefficient of rhombus pattern is the greatest one among that of the three laser patterns. The friction coefficient of longitudinal and transverse pattern is almost the same, but the former is a little higher than that of the latter. The friction coefficient is mainly depended on the ratio of asperity contact pressure to the total pressure in mixed lubrication. The orientation effect on friction coefficient is also determined by lateral flow which is highly depended on the geometry of contact region.

2016, 48(5): 1114-1125. doi: 10.6052/0459-1879-16-080

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AN IMPROVED METHOD OF THE CALCULATION OF EQUIVALENT NODAL FORCES IN VISCOUS-ELASTIC ARTIFICIAL BOUNDARY

Zhang Xiaolong, Li Xiaojun, Chen Guoxing, Zhou Zhenghua

The viscous-elastic artificial boundary is widely used in the analysis of site seismic response and dynamic structure-soil system interaction problems. Seismic input is usually taken as equivalent nodal forces incorporating in the viscous-elastic artificial boundary, and stress in the control area of any artificial boundary node in the conventional method is considered as uniform distribution. However, its distribution is actually uneven. An improved method is proposed for the seismic input of wave propagation scattering problem in infinite domain. In the proposed method, an viscous-elastic artificial boundary is first introduced; seismic input is considered as the equivalent node forces to be incorporated directly in these local boundaries, and the node force obtained using the mesh refinement process combining stress integration of adjacent node regions is changed along the artificial boundary nodes, and its computation error is effectively reduced; the two-dimensional wave propagation problem in time-domain is then solved using the explicit finite element method. The numerical simulation of two-dimensional finite element site models of wave propagation problem with various mesh sizes and incidence angles are presented to demonstrate the performance of the improved method in this paper. The simulating nephogram of wave propagation and values of response displacement show that the calculating precision of the improved method is closely related to the mesh size and wave incidence angle, and increases with decrease of the mesh size and incidence angle. The simulation result also shows that the calculating precision of the improved method is significantly higher than that of the conventional method in the case of the same mesh size and incidence angle.

2016, 48(5): 1126-1135. doi: 10.6052/0459-1879-16-070

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ANALYTICAL MODEL FOR SHEAR STIFFNESS OF REINFORCED CONCRETE BEAM WITH STIRRUPS

Zheng Kaiqi, Liu Zhao, Qin Shunquan, Zhou Man

The calculation of deflection of reinforced concrete (RC) beams generally ignores the contribution of shear deformation. However, diagonal crack will significantly reduce the effective shear stiffness of RC beams, and result in remarkable increase of shear deformation, which should not be neglected in the assessment stage. To evaluate the effective shear stiffness of diagonally cracked RC beams with stirrups, an analytical model of shear stiffness was proposed in the paper. Firstly, the shear stiffness of RC beam at stirrup yielding status was derived based on variable angle truss model. Compared to the elastic shear stiffness, the shear stiffness degradation factor was mainly influenced by the material modulus ratio, stirrup ratio and the inclination angle of strut. Secondly, based on the observed shear stiffness degradation law of shear deformation curve, a constant tangent stiffness degradation mode, which considers the influence of cracking level, was proposed. The shear increment after shear cracking was used as a quantitative indicator for the cracking level. Finally, the analytical formulas of the inclination angle and shear stiffness degradation factor were obtained based on the principle of minimum strain energy. To verify, two thin-webbed concrete beams were tested and corresponding shear deformation were carefully measured. In addition, shear deformation data of fifteen shear segments of RC beams in literature were collected. The comparison results showed that the proposed shear stiffness degradation model gives good prediction of the shear stiffness at stirrup yielding status and reflects the degradation law of shear stiffness at different cracking level.

2016, 48(5): 1136-1144. doi: 10.6052/0459-1879-15-371

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DISCUSSION ON THE MATRIX PROPAGATOR METHOD TO ANALYZE THE RESPONSE OF SATURATED LAYERED MEDIA

Zhao Yunxin, Chen Shaolin

Seismic response analysis of horizontal layered soil is the precondition of the seismic wave scattering problem. The previous studies mostly focused on the dry soil condition, but in practical engineering, below the underground water level, the soil is filled with fluid. So the saturated porous media model should be considered. Based on the Biot model, considering the attenuation caused by the relative motion of solid and liquid, the steady-state response of saturated layered soil subjected to oblique incident seismic wave is obtained by using the Thomson-Haskell propagator matrix method. The time-domain transient response can be obtained by inverse Fourier transform. This method is validated by a numerical example that SV wave is incident from the bedrock to the overlying saturated soil layers. Two kinds of contraries to law of causality are found in numerical analysis, and their reasons are explained preliminarily:(1) When the incident angle of SV wave is larger than the critical angle for the reflection P wave in the bedrock becoming non-uniform, it leads to noncausality; (2) Due to the attenuation of P2 wave, when the attenuation coefficient associated with the parameters such as permeability, the thickness of the soil layer and the frequency of the incident wave is beyond the computer accuracy, it leads to noncausality either. The range of parameters necessary for causality is obtained accordingly, which can be used as an upper bound in practice. This work provides guidance for the analysis of free field response of saturated soil layer.

2016, 48(5): 1145-1158. doi: 10.6052/0459-1879-16-029

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AN ELASTOPLASTIC CONSTITUTIVE MODEL OF CONCRETE UNDER COMPLICATED LOAD

Wan Zheng, Yao Yangping, Meng Da

A prominent variety of stress-strain relationships are displayed for concrete under different stress paths or complex loading conditions. A stress-strain relationship similar to the elastic deformation of the hysteresis loops is observed under a small amplitude of deviatoric stress. The stress-strain relationship and failure behavior are associated with the value of hydrostatic pressure under different stress paths. The prominent of anisotropic behavior is weakening with increasing the value of hydrostatic pressure. In addition, the failure mechanisms and the corresponding hardening damage processes of compression and tension, are all different. There are three hardening damage types, namely the compressive hardening damage, tensile hardening damage and the mixing hardening damage. A new model is proposed by revising Hsieh model at three aspects:(1) There is not plastic deformation for small amplitude of deviatoric stress under cyclic loading conditions, while there is always plastic deformation predicted by Hsieh model. The frame of bounding surface model is adopted and a pure elastic zone is established in the bounding surface. The assumption that the initial yield surface and subsequent critical yield surface is similar in geometry is adopted. (2) A generalized constitutive model is proposed by transformed stress method based on generalized nonlinear strength criterion. The hydrostatic pressure effect of meridian plane and deviatoric plane for different stress paths can be reasonably considered by adopting the proposed model. A problem of singular stress point on boundary surface is avoided by adopting the TS method. (3) Hardening parameter expressions based on two kinds of load in tension and compression damage pattern are proposed and can be respectively adopted to describe the strain softening and strength degradation behavior generated by loading process. The proposed model can be used to describe the general stress-strain relationship of concrete based on a variety of loading tests simulation.

2016, 48(5): 1159-1171. doi: 10.6052/0459-1879-15-389

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A RECURSIVE ABSOLUTE NODAL COORDINATE FORMULATION WITH O(n) ALGORITHM COMPLEXITY

Hu Jingchen, Wang Tianshu

Compared with the tradition floating frame of reference formulation, the absolute nodal coordinate formulation (ANCF) has a natural advantage in solving nonlinear large deformation problems. However, the mathematic model established by ANCF is always converted to differential algebraic equation (DAE) based on analytical mechanics methods, which leads to an O(n²) or O(n³) algorithm complexity and position or speed constraint violation during the solution procedure. In order to solve these problems, this paper proposes a recursive absolute nodal coordinate formulation (RANCF) with O(n) algorithm complexity. Firstly, the flexible bodies are described by RANCF. Secondly, a kinematic and dynamic recursive relationship between adjacent elements in the flexible multibody system is established based on the articulatedbody algorithm (ABA). The equation obtained by RANCF is an ordinary differential equation (ODE), and the system generalized mass matrix is a tridiagonal block matrix. Thus, a recursive solution of the equation by element could be obtained through an appropriate matrix processing. On this basis, a particular algorithm flow of RANCF is provided with the efficiency of each step analyzed in detail, which proves the RANCF is an O(n) complexity algorithm. The RANCF maintains the advantage of ANCF that can accurately solve large deformation multibody problem, and vastly improves the computational efficiency of ANCF. In addition, because the ANCF avoids the constraint violation problems of DAE, it also has a higher algorithm accuracy. Finally, the validity and effciently of this method is verified by the MSC.ADAMS software, the energy conservation test and the DOF-CPU time test.

2016, 48(5): 1172-1183. doi: 10.6052/0459-1879-16-117

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EQUIVALENT CIRCULAR RING MODEL FOR THE RADIAL VIBRATION ANALYSIS OF HOOP TRUSS STRUCTURES

Liu Fushou, Jin Dongping

In large deployable mesh antenna, the dynamic property of hoop truss is vital to the working performance of the whole antenna. For large space truss structures, the model simplification of these structures with simple elastic continuum model is always the focus of dynamics research. By regarding the hoop truss as a hoop periodic structure composed of repetitive planar truss elements, and based on the equivalent beam model of the repeated truss element, an equivalent circular ring model for the radial vibration analysis of the hoop truss structure is presented. By variable substitution, the fourth-order partial differential equations (PDEs) for the radial vibration of theffcircular ring are reduced to first-order PDEs, then the reduced PDEs are transform to ordinary differential equations via Laplace transform, Green's function method is utilized to solve the dynamic response of theffcircular ring in complex frequency domain. Furthermore the characteristic equations for natural vibration and the expression of transfer function of the equivalent ring model were derived. At last, a numerical example is used to compare the natural frequencies, mode shapes and transfer functions of the finite element model and the equivalent ring model of the hoop truss. The results verifies the feasibility of using equivalent circular ring model for radial vibration analysis of hoop truss structure.

2016, 48(5): 1184-1191. doi: 10.6052/0459-1879-16-076

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NONLINEAR BIFURCATION ANALYSIS OF LATERAL LOSS OF STABILITY FOR HYPERSONIC VEHICLE

Su Erlong, Luo Jianjun

Aiming at addressing the loss of stability in lateral motion of hypersonic gliding vehicle with high angle of attack, the bifurcation theory and the continuation approach were used to obtain the branches of the steady equilibria where the elevator was considered as a continuation parameter. Meanwhile, the lateral maneuver branches of equilibria were also computed where the aileron was employed as a continuation parameter for the selected characteristic points. Then, the stability and bifurcation points were analyzed in detail, and the topologies for the 5 dimension model were given. It was found that the limit points, Hopf points and branch points exist for the branches. The pitchfork branches were stretched out from the BP points where the loss of stability for auto-rotation was triggered; the branches extending out from the Hopf point were also researched in detail where the complicated limit circle motion was presented involving perioddoubling bifurcation, Neimark-Sacker bifurcation, limit point of circle bifurcation etc.; furthermore, through analyzing the branches of equilibria for lateral maneuver condition, problems of loss of stability for maneuver, multi-equilibrium points and loss of stability for lateral control dynamics exist. The results of the research could provide the important dynamic information for realizing the flight stability and designing of the controller.

2016, 48(5): 1192-1201. doi: 10.6052/0459-1879-15-388

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DUAL VARIABLE VARIATIONAL METHOD FOR NONLINEAR LEAST SQUARES SHADOWING PROBLEM

Xun Guangbin, Peng Haijun, Wu Shunan, Wu Zhigang

The least squares shadowing (LSS) method, to compute the shadowing trajectories of dynamical systems, has been presented in recent years. The ill-posed initial value problem within the conventional sensitivity analysis algorithm for nonlinear systems can be effectively avoided based on the LSS method, which therefore has significant applications in the sensitivity analysis of chaotic systems. To achieve nonlinear LSS problem, it will be firstly represented as a nonlinear optimal control problem subject to constraints. By introducing the costate variables, the Hamiltonian function is represented depending on state and costate variables. The integral time of objective function is then discretized, and the state variables at ends of time interval are taken as independent variables. Then approximate the state and costate variables in the time interval using the Lagrange polynomials. This problem is finally transformed into solving nonlinear equations via dual variable variation principle. The linearizing process is avoided for the proposed algorithm, and then the errors, caused by the complex linearizing process, are also reduced, which provides affinew solution for solving the shadowing problem. Two state trajectories with designing parameters slightly changed can be obtained by LSS problem, and then the sensitivity of the nonlinear system is calculated from the two trajectories. Van der Pol oscillator as a numerical example shows that this method is effective for the LSS problem and sensitivity analysis of nonlinear systems.

2016, 48(5): 1202-1207. doi: 10.6052/0459-1879-15-399

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A CANALICULAR FLUID FLOWMODEL ASSOCIATED WITH ITS FLUID FLOWRATE AND FLUID SHEAR STRESS

Wu Xiaogang, Yu Weilun, Wang Zhaowei, Wang Ningning, Cen Haipeng, Wang Yanqin, Chen Weiyi

Stressed bone can be deformed to lead to an interstitial fluid flow or diffusion in its microstructure-osteon (wall). Actually in this fluid diffusion process, some physical effects related with fluid stimuli are induced, such as fluid shear stress (FSS) and streaming potential. These effects may enable the bone cells to detect and respond to the process of bone-resorbing and bone-forming to adapt the external loading environment. Due to the limitation of experimental approach, theoretical simulation has become the main method to study the bone's interstitial fluid flowing behavior. Based on the poroelasticity, a physical canaliculi model is developed to link the mechanical loading on osteon scale to the scale of canalicular fluid flow, which makes a significant step to study the mechanism of the bone mechanotransduction and electromechanotransduction. This developed canaliculi model is based on a hollow osteon model and a Haversian fluid considered osteon model, with two boundary cases on the outer wall, elastic restrained and rigid confined. Finally, the analytical solutions for canalicular fluid flow rates (FFR) and shear stress are obtained. The results predict that the amplitudes of fluid flow rate and shear stress are proportional to strain amplitude and frequency. However, the key loading factor governing canalicular fluid flow behavior is the strain rate, which is a representative loading parameter under a physiological state. The larger canalicular radius is, the larger amplitudes of FFR and FSS generalized, especially, the FSS amplitude is proportional to canalicular radius. The Haversian fluid can enhance the whole canalicular fluid flow rates and shear stress fields.

2016, 48(5): 1208-1216. doi: 10.6052/0459-1879-16-046

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EFFECT OF WATER DISTRIBUTION ON METHANE ADSORPTION CAPACITY IN SHALE CLAY

Li Jing, Li Xiangfang, Wang Xiangzeng, Xin Yinan, Han Junfeng, Shi Juntai, Sun Zheng, Wang Rui

Methane adsorption in shale is the result of gas-liquid-solid interaction when considering water saturation in actual condition. And the moisture (water saturation) which significantly influences methane adsorption capacity will likely make shale gas resources misestimated. In this paper, we analyze the interaction characteristics between methane, water film and clay base on adsorption theory, and results reveal that:(1) methane adsorption on clay (dry) could be described by gas-solid interface Langmuir adsorption equation; (2) methane adsorption on water film could be described by gas-liquid interface Gibbs adsorption equation; (3) gas-liquid-solid interaction could be described by ‘gas-solid’ and ‘gas-liquid’ integrated equation. Meanwhile, we find that water saturation distribution is significantly effected by pore size, and micropores could be filled with water in certain condition while macropore only bound by water film. Therefore, the influence of moisture on methane adsorption is mainly for two aspects:(1) micropores which blocked by water are invalid for methane adsorption; (2) macropores bounded by water film change the interaction characteristics for methane adsorption (from gas-solid interaction to the gas-liquid interaction), and the overall effect could decrease the adsorption capacity by 90% in our study. Our present work reveals mechanism of moisture effect on the shale absorption capacity and lays the foundations of evaluating the adsorbed gas in shale gas reservoir more accurately.

2016, 48(5): 1217-1228. doi: 10.6052/0459-1879-15-452

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HYDRAULIC FRACTURE PROPAGATION IN SHALE GAS BEDDING RESERVOIR ANALYTICAL ANALYSIS

Sun Keming, Zhang Shucui

Shale gas deposits in shale reservoirs, whose bedding structures are different from conventional heterogeneous reservoirs. This also makes the shale reservoirs have different crack propagation laws in hydraulic fracturing. In order to investigate the crack propagation laws of shale reservoir hydraulic fracturing, complex variable function and conformal transformation is adopted here to deduce the solutions of crack tip stress concentration. The fracture propagation criterions have been put forward when the perpendicular to the minimum in-situ stress hydraulic fracture meets oblique bedding by considering shale reservoirs heterogeneity as well as strength anisotropy and then comparing fluid pressure satisfied fracture propagation in all directions. In order to show how difficult the hydraulic fracture turning to bedding, the critical strength ratios of bedding and rock mass are defined respectively when the fracture just initiates in bedding and propagates along bedding. Based on these two critical strength ratios, the bedding strength range which fracture initiates in bedding and propagates along bedding can be obtained. Analytical analysis show as follows:the critical strength ratio of bedding crack initiation increases with the decrease of bedding strike angle and dip angle and the increase of min-principal stress and the rock strength. The critical strength ratio of bedding crack initiation increases when the max-principal stress decreases and the middle-principal stress increase if the strike angle is less than 35.26°. Otherwise the critical strength ratio of bedding crack initiation decreases when the max-principal stress decreases and the middle-principal stress increase if the strike angle is greater than 35.26°. The critical strength ratio of bedding crack propagation increases when bedding strike angle, dip angle and in-situ stress difference decrease and the rock strength increase. Only when the critical conditions of bedding crack initiation and propagation all are satisfied do the hydraulic fractures turn to bedding.

2016, 48(5): 1229-1237. doi: 10.6052/0459-1879-16-085

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A NEW EXPLOITATION METHOD FOR GAS HYDRATE IN SHALLOWSTRATUM: MECHANICAL-THERMAL METHOD

Zhang Xuhui, Lu Xiaobing

Gas hydrate is one of the national strategic energy resource. The endothermic chemical dissociation and phase transformations make its exploitation differ from those of the fossil energies. A continuous, stable, and high effcient heat supply is the critical problem to commercial production of gas hydrate. The combined mechanical-thermal gas hydrate exploitation is affinew conceptual method, crushing gas hydrate-bearing sediments into small bodies to increase the surface area of heat transfer, and utilizing the heat of seawater and convective heat transfer to enhance the efficiency of energy supply. Through the feasibility analysis, the results show that relative high temperature leads to the rapid dissociation of gas hydrate, and the fluid flow becomes unstable, while low temperature leads to the reformation of gas hydrate or freezing. In order to achieve effcient and safe exploitation of gas hydrate, the diameter of crushing bodies of in-situ mining hydrate-bearing sediments ranges from 0.1 cm to 1.0 cm, the seawater injection velocity ranges from 0.22m/s to 0.67m/s, the temperature difference is greater than 5 K, and the volume fraction of water in the mixed water and grains of hydrate sediments exceeds 0.85. The combined mechanical-thermal hydrate exploitation is affinew potential technology for effcient production of gas hydrate stratums.

2016, 48(5): 1238-1246. doi: 10.6052/0459-1879-15-112

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THE SUPPORTED PROJECTS ON MECHANICS OF NSFC IN 2016

Zhan Shige, Zhang Panfeng, Sun Zhongkui, Wang Jianshan

The paper brief introduced the supported NSFC projects for General Programs, Young Scientists Fund, Fund for Less Developed Regions on mechanics in 2016. The projects list is also given.

2016, 48(5): 1247-1264. doi: 10.6052/0459-1879-16-238

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2016 Vol. 48, No. 5

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