力学学报

STUDIES ON AEROELASTIC ANALYSIS AND CONTROL OF AIRCRAFT STRUCTURES

Hu Haiyan, Zhao Yonghui, Huang Rui

The development of active control has witnessed a great change in the design of aircraft structures, from the passive design of increasing structure sti ness to the active design in view of control configured aircraft. The idea of active design does not intentionally avoid the aeroelastic problem, but adjust the structural aeroelasticity via active control so as to reduce the structure weight and optimize the aircraft performance. To achieve this purpose, it is necessary to analyze the coupling between the aircraft structure and surrounding aerodynamic loads. The aeronautical community has made great e orts to study the corresponding aeroelastic problems and gain an insight into the coupling among aircraft structure, aerodynamics and active control since 1980's. However, most studies have been based on the simplified models. As such, it is di cult to apply the research achievements to aeronautical industry. This review article surveys the recent advances in the dynamic problems of aircraft aeroelasticity including the aerodynamic nonlinearity, the backlash nonlinearity of control surfaces, instability induced by time delay in control loop, active flutter suppression, gust load alleviation, as well as corresponding wind tunnel tests. The review focuses on the new approaches proposed by the team of authors, and the corresponding numerical simulations and wind tunnel tests over the past decade. Finally, the review addresses a number of open problems related to the aeroelastic analysis and control.

2016, 48(1): 1-27. doi: 10.6052/0459-1879-15-423

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2016, 48(1): 28-28.

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MESO-STRUCTURE INFORMED EFFECTIVE STRESSES IN SATURATED AND UNSATURATED POROUS MEDIA

Li Xikui, Du Youyao, Duan Qinglin

Based on the meso-strucrured Voronoi cell model and the meso-macro homogenization procedure between the discrete particle assembly and the porous continuum for wet granular materials, the e ective stresses in saturated and unsaturated porous media are defined. The generalized e ective stress for saturated porous continua taking into account the volumetric deformation of solid grains due to pore liquid pressure are derived. The Biot coe cient introduced to define the generalized e ective stress depends on not only the bulk moduli of both the porous media and the solid grains (material parameters), but also the current mean stress of solid skeleton of porous media and the current volumetric strains of the individual grain due to the hydrostatic pressure (state variables). The wet meso-structured Voronoi cell model, consisting of three immiscible and interrelated (i.e., solid grains, interstitial liquid and gas) phases, is proposed. The meso-structural pattern with the binary bond mode of pendular liquid bridges valid at low bulk saturation is particularly assumed to derive the meso-hydro-mechanically informed anisotropic e ective pressure and e ective stress tensors for unsaturated porous media. As the isotropic case of the wet meso-structured Voronoi cell model is considered, the meso- hydro-mechanically informed e ective pressure tensor degrades to the scalar variable in the form as same as that given in the theory of unsaturated porous continua. The proposed meso-hydro-mechanically informed Bishop's parameter is derived and obtained as a function of the saturation, the porosity, meso-structural parameters, while without the need to introduce any phenomenological assumptions.

2016, 48(1): 29-39. doi: 10.6052/0459-1879-15-289

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A MODIFIED NONLOCAL RHEOLOGY MODEL FOR DENSE GRANULAR FLOW

Ye Xiaoyan, Wang Dengming, Zheng Xiaojing

In dense granular flows, a non-local rheology theory was proposed by Pouliquen et al. based on the idea of a self-activated process, in which a rearrangement at one position will be trigged by stress fluctuation due to rearrangements elsewhere in the material. Taking into account the probability density distribution of stress fluctuation amplitude in granular materials and the coupling e ect between shear rate and volume fraction in iterative calculation, a modified non-local rheological model was proposed in order to describe the dense granular flow more accurately. Due that dense granular flows down inclines preserve this complexity but remain simple enough for detailed analysis, this modified model was applied to predict the rheological characteristics of flows down a rough inclined plane. Compared to the previous non-local rheological model, the predicted results based on the present modified model, including the critical thickness, depth-averaged velocity and shear rate profile, are quantitatively better consistent with the existing experimental and simulating results.

2016, 48(1): 40-47. doi: 10.6052/0459-1879-15-287

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STUDIES ON THE TRANSITION BETWEEN SOLID- AND FLUID-LIKE STATES OF GRANULAR MATERIALS

Fei Minglong, Xu Xiaorong, Sun Qicheng, Zhou Gordon G D, Jin Feng

Not like the traditional fluid or solid, granular media is a combination of large amounts of discrete particles, which may lead to the coexistence of di erent flow regimes and their complex transitions between each other in granular media during its movement. Elastic instability and irreversible flow rule are the keys to understand the mechanical behaviours of granular solid and granular fluid, and especially the phase transition from granular solid to granular fluid. In this paper, we deduced the instable critical condition for instant elastic energy based on the two-granular-temperature thermodynamics (TGT) for granular media, and developed a related irreversible flow rule, with a MPM numerical model we built and used it to simulate a sandpile collapsing, which is a typical transition process between granular solid and granular fluid. Physical experiment and DEM simulation were carried out for comparison, and both numerical results can march well with those from the experiment. We also found out some disadvantages for TGT model and MPM. In this work, the sand dam developed from static compression to irreversible flow after failure, then finally deposited again, and the TGT model and MPM shows the capacity of describing the solid- and fluid-like behaviour, and the phase transition of granular media well during the sandpile collapse.

2016, 48(1): 48-55. doi: 10.6052/0459-1879-15-290

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PERIDYNAMICS SIMULATION FOR DYNAMIC RESPONSE OF GRANULAR MATERIALS UNDER IMPACT LOADING

Zhang Qing, Gu Xin, Yu Yangtian

The dynamic mechanical behavior of granular materials under impact load is a complex issue. Peridynamics as a new theory based on discontinuous and nonlocal hypothesis regards materials as compositions of massive material points with finite volume and finite mass, and builds an integral governing equation to reflect the motion law of material points. For all the features mentioned above, peridynamics is certainly suitable for describing and analyzing the dynamic behavior of particles. An improved PMB model considering the feature of nonlocal long range force and eliminating the “boundary e ect” and a repulsive force model at material point level to describe the inter-particle contact interaction are proposed. Then the method is applied to analyze the dynamics responses of tungsten carbide (WC) ceramic granular system su ering from impact loading. Wave velocities of the system were calculated accurately under di erent impact velocities compared with the experiment results. Phenomena of the motion, including translation and rotation, deformation and crushing of particles are reappeared. There are both total damaged particle and slight damaged particle near the impactor, and there are also particles far out from the impactor which are damaged. The extrusion, collision and shear slide between particles result in the particle crushing. The results indicate that the calculation model and analysis method developed here can well reflect the dynamic behavior of granular materials and have large application value.

2016, 48(1): 56-63. doi: 10.6052/0459-1879-15-291

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THE SEGREGATION AND MIXING OF BINARY GRANULAR SYSTEMS IN ROTATING MIXER WITH DIFFERENT CROSS-SECTIONS

Yan Ming, Duan Wenshan, Chen Qiong, Zhou Zhigang, Zhang Yu, Zhao Chuang, Hou Meiying

The effects of filling conditions and angular speeds of circle, ellipse and square mixers on segregation and mixing are studied adopting theoretical, experimental and simulation approaches. Different segregation and mixing patterns of granular material can be obtained by changing the angular speed or filling conditions in experiments. From the analysis of trajectory of tracer particles, we find that particles' motion randomness in radial direction decreases with the angular speeds augment, and contrast results occur in rectangular mixer. The simulation results show that the flow consists of two distinct regions: a flowing layer with nearly unidirectional flow and a bed below it undergoing solidbody rotation. Through theoretical analysis, we find the segregation phenomenon is most apparent in circle mixer, then in the ellipse mixer, and the weakest is in rectangular mixer.

2016, 48(1): 64-75. doi: 10.6052/0459-1879-15-292

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PARTICLE-DEM BASED LINKED BAR STRAIN SOFTENING MODEL AND ITS APPLICATION

Feng Chun, Li Shihai, Liu Xiaoyu

Based on finite contact assumption between particles, a linked bar model to transmit the force and moment between particles is proposed. To represent the plastic, damage and fracture process of linked bar, the Mohr-Coulomb model and maximal tensile stress model considering strain softening e ect is introduced. The numerical results of uniaxial extension test and direct shear test with single linked bar show the accuracy of the model. The relationship between equivalent macro strain energy of particles system and the average coordination number is studied. Numerical results show that, for 2D particles system, when the average coordination number equals 5, the equivalent macro strain energy of particles system coincides well with the strain energy computed by approaches based on continuous media (i.e. FEM). The uniaxial compression process of rock is simulated based on the linked bar strain softening model. The results show that, the strain-stress curve of rock during uniaxial compression could be divided to four stages, which are linear stage, hardening stage, softening stage and sliding stage, and the relationships between four stages and damage fracture status of rock are also studied. From the results, with the increase of fracture strain, the failure mode of rock changes from tensile-shear composite fracture pattern to purely compression shear fracture pattern. With the increase of fracture strain, the peak stress and corresponding critical strain increases gradually, however, the fracture degree at peak point and at final state decreases gradually.

2016, 48(1): 76-85. doi: 10.6052/0459-1879-15-288

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EXPERIMENTAL INVESTIGATION OF BUBBLE EVOLUTION ON ANNULAR NOZZLE

Hu Jun, Jiang Jianyu, Yu Yong, Li Tingting

The Evolution and dynamic behavior of bubble underwater is an important theory basis for the gas-liquid two-phase flow and application of underwater jet. The forming bubble and gas jet through annular nozzle have di erent performances and mechanism with bubble and jet generate through round hole. With the requirement of special application such as the concentric cylinder water piercing missile launching, observing the basic phenomena and mechanism analysis of the annular nozzle gas jet / bubble flow become an urgent need. A set of experimental system of the annular nozzle were designed and the evolution of bubbles through the annular nozzle was investigated. The visualization of bubble flow was realized by a high speed camera, which was used to record the bubble growth process. The bubble formation regimes, the influence of gas flow rate on bubble formation periods and bubble volume were studied based on the image processing and analysis of flow field.The experimental results indicate that: the regime of bubble formation is a period-3 bubbling under air flow rate from 50.8 dm³/min to 237.3 dm³/min; The variation of bubble formation periods and bubble volume with gas flow rate was given, which indicates that bubble formation periods and bubble volume are strongly dependent on the gas flow rate. Because of the cooperation of the surface tension, water inertia and liquid flow, top of the bubble will collapse downward during formation. It will lead to form an toroidal bubble.

2016, 48(1): 86-94. doi: 10.6052/0459-1879-15-183

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AN APPLICATION OF IMPLICIT GAS-KINETIC UNIFIED ALGORITHM BASED ON MULTIBLOCK PATCHED GRID

Peng Aoping, Li Zhihui, Wu Junlin, Jiang Xinyu

Gas Kinetic Unified Algorithm (GKUA) based on Boltzmann model equations is proposed for simulating aerodynamics problems covering various flow regimes. In this algorithm, molecular motions are decoupled from collisions by traditional Computational Fluid Dynamics methods, so that the calculation e ciency would be quite low at the limitation of stabilization conditions of explicit schemes when simulating supersonic flows especially which are near-continuum and continuum flows. In order to improve the e ciency and expand engineering practicability, an implicit method for Boltzmann model equations is constructed by using LU-SGS (Lower-Upper Symmetric Gauss-Seidel) method and cellcentered finite volume method, and multi-block patched grid technique is used in physical space. The present computed results of two side-by-side cylinders in transitional flow regime are found in good agreement with those from Direct simulation Monte-Carlo method simulation. The dependability and feasibility for simulating problems covering various flow regimes by the present method are validated.

2016, 48(1): 95-101. doi: 10.6052/0459-1879-14-279

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THEORETICAL INVESTIGATION ON AERODYNAMIC FORCE MEASUREMENT INTERFERED BY STRUCTURAL VIBRATIONS IN LARGE SHOCK TUNNEL

Meng Baoqing, Han Guilai, Jiang Zonglin

Structural vibration of aerodynamic measurement system is caused by the impulse forces generated by startup process of the shock tunnel, and the test time is too short to allow the vibration to decay. Therefore, the aerodynamic force measurement can be considered as a dynamic process, during which the signals outputted by balance are consist of aerodynamic force signals and vibration signals. Existing methods are lack of support of theory and the accuracies of them are limited. Theoretical analysis is used in this paper and we obtain the analytical solutions of fundamental characteristics of free vibrations and forced vibrations. Study of free vibrations focuses on the disciplines of aerodynamic force measurement interfered by a single vibration shape and amplitude of interference changed with section of force measurement. The inferences of di erent vibration shapes during forced vibration motivated by varied forces are investigated in research of forced vibration. Results show that there are theoretical defects for traditional acceleration compensation techniques because the zero points of amplitude of interference and acceleration are inconsistent. What's more, the influences of section for force measurement, acting position of force and type of force should be considered to determine the main source of interference in experiments.

2016, 48(1): 102-110. doi: 10.6052/0459-1879-15-152

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EFFECTIVE COUPLE-STRESS DYNAMIC BEAM MODEL OF A TYPICAL CELLULAR SOLID

Su Wenzheng, Liu Shutiany

The e ective continuum beam model can be used to study the dynamic behavior of the one-dimensional cellular solid structure. However, this e ective model will bring the size e ect when the cell size is close to the height dimension of the beam-like structure. The classical continuum model, which has no length scale, cannot describe this size dependent feature. By contrast, the generalized continuum model is pertinent to the description of the size e ect. The purpose of this paper is to develop an e ective Timoshenko continuum beam model for the transverse natural vibration analysis of a periodic cellular solid beam-like structure whose unit cell has a circular void, based on the couple-stress theory. The properties of the e ective couple-stress continuum are generated under the criterion of the equivalent strain energy and the geometrical average by the analysis of a unit cell. These properties are then employed in the Timoshenko beam theory to obtain the dynamics di erential equations. Comparison is made with the prediction of a finite element analysis of the complete cellular structure, which is taken as the benchmark for accuracy. Good agreements both on the frequencies and mode shapes are found by a variety of examples where the method of modal assurance criterion (MAC) is employed for the comparison of the mode shapes. The emphasis is put on the influence of the relative size of the void diameter, the size ratio of the beam height to the cell size, and the aspect ratio of the beam-like structure on the accuracy of the e ective beam model. A series of methods on the natural vibration analysis of a cellular solid beam-like structure is recommended conservatively based on these analyses.

2016, 48(1): 111-126. doi: 10.6052/0459-1879-15-210

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GRADIENT TYPE OF NONLOCAL HIGHER-ORDER BEAM THEORY AND NEW SOLUTION METHODOLOGY OF NONLOCAL BENDING DEFLECTION

Chen Ling, Shen Jiping, Li Cheng, Liu Xinpei

Di erent predictions were found in di erent literatures about the trend of nonlocal e ects on nanostructural sti ness. By employing an iterative method and the Taylor expansion method, an infinite series for nonlocal high-order stress is achieved based on the gradient-type of nonlocal di erential constitutive model. The nonlocal stress consists of the classical bending stress and each order gradient of nonlocal deflection. Consequently, the di erential equation of the bending deflection curve for nonlocal high-order beam is derived. The nonlocal deflection is determined via the regular perturbation method. Some numerical examples are provided to reveal and quantize the e ects of nonlocal scale factor on bending deflection. It is shown that compared with the corresponding classical results, the nonlocal bending deflections of nanostructure may increase, decrease or remain unchanged. The sti ness of nanostructures can be reduced or enhanced or the same as classical structures by considering the gradient-type of nonlocal high-order stress e ect, and the trend depends on external loads and boundary constraints which are found to play significant roles independently in nonlocal bending of nanostructures. Moreover, it is observed for the first time that the position of maximum nonlocal deflection may be influenced by nonlocal scale factor. The present studies are expected to solve the problems in the application of nonlocal elasticity theory to nanostructures, and further provide supports for the development and optimization of such theory.

2016, 48(1): 127-134. doi: 10.6052/0459-1879-15-170

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ANALYSING THEWAVE SCATTERING IN SINGLE-WALLED CARBON NANOTUBE CONVEYING FLUID BASED ON THE SYMPLECTIC THEORY

Li Yuan, Deng Zichen, Ye Xuehua, Wang Yan

Based on tcontinuum mechanics theory and the symplectic theory, the single-walled carbon nanotube (SWCNT) is modelled as a Timoshenko beam. The dynamics equations of fluid-conveying SWCNT are derived from Hamilton's principle. By introducing the symplectic variable into the mechanics system, the governing equation of fluid-conveying SWCNT is transformed from Lagrange system into Hamilton system, then the governing equation is employed to analyse the energy band structure of the SWCNT and the wave scattering in the beam. Moreover, the scattering matrix of the nanotube is calculated by symplectic methodology. The influences of the fluid density and velocity to SWCNT's band structure are also analysed. The results show that the shear and flexural frequencies of SWCNT are greater than those of fluid-conveying SWCNT. The analyses indicate that the shear and flexural frequencies of fluid-conveying SWCNT decrease with the fluid velocity and density increasing, because the e ect of the fluid inside makes the nanotube softer. Meanwhile, it is also found that the scattering matrix is unitary matrix, pointing the power flow of the incident wave is equal to that of the reflected wave, indicating the power flow of Hamilton system is conserved. Furthermore, the results show the superiority of the symplectic elasticity theory.

2016, 48(1): 135-139. doi: 10.6052/0459-1879-15-164

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AN ANISOTROPIC VISCO-HYPERELASTIC CONSTITUTIVE MODEL FOR CORD-RUBBER COMPOSITES

Huang Xiaoshuang, Peng Xiongqi, Zhang Bichao

Based on fiber reinforced continuum mechanics theory, an anisotropic visco-hyperelastic constitutive model for cord-rubber composites was developed to characterize their highly non-linear, strongly anisotropic and strain rate dependent mechanical behaviors under high speed impact or large deformation condition. The unit-volume strain energy function for the visco-hyperelastic model was decomposed into four parts, representing the strain energy from isochoric rubber, the tensile energy from cord elongation, shearing energy from interaction between cord and rubber and viscous potential energy due to viscous characteristics, respectively, which greatly facilitated and simplified the identification of material parameters. By introducing the so called viscous potential energy that could not be neglected under particular loading conditions, the computation accuracy of the model was significantly improved. A simple approach for fitting the parameters was given. Experimental data from literature was used to identify material parameters in the constitutive for a specific cord-rubber composite. The developed model was validated by comparing numerical results with experimental uniaxial tension and bias-tension data under di erent strain rates, demonstrating that the developed constitutive model is highly suitable for characterizing the anisotropic and viscous material behaviors of cord-rubber composites under large deformation. The proposed model is simple, useful and easy for material parameter determination. It provides a theoretical foundation for dynamic finite element analysis of tire in the future.

2016, 48(1): 140-145. doi: 10.6052/0459-1879-15-189

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PREDICTION OF FORMING LIMIT OF BORON STEEL AT ELEVATED TEMPERATRUE BASED ON CDM THEORY

Tang Bingtao

To meet the requirement of energy saving and automobile safety, more and more attentions are paid to the development and application of high strength steels. Hot stamping of ultra high strength steel is an important way to reduce the weight of body-in-white, improve the anti-impact and anti-collision performance of the vehicle, and has become a hot technology in the world wide. The forming limit is a very important parameter in boron steel hot stamping process. Due to the complexity of the Nakazima test at elevated temperature, there are a lot of problems to be solved. In the paper, the ductile damage model and finite element simulation technology were combined to predict the forming limit of boron steel at elevated temperature. Based on the continuum damage mechanics (CDM), the Lemaitre ductile damage model considering the e ect of e ective stress and e ective plastic strain on evolution of microvoid was established. In order to accurately predict the formability of boron steel at elevated temperature, a modified dissipation potential coupling the e ect of plastic strain was introduced. Genetic Algorithm-II (NSGA-II) was integrated with finite element software FORGETM to find the optimized ductile damage parameters. The obtained damage parameters can accurately predict the sheet instability and fracture behaviour in tensile test. The established ductile damage model is introduced in the simulation of Nakazima test with boron steel. The comparison between the predicted forming limit and that of experiment witnesses the reliability of the forming limit prediction at high temperature using the proposed ductile damage model.

2016, 48(1): 146-153. doi: 10.6052/0459-1879-15-314

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INTERFACE CRACKING ANALYSIS WITH INCLUSIONS INTERACTION IN COMPOSITE CERAMIC

Fu Yunwei, Zhang Long, Ni Xinhuay, Liu Xiequan, Yu Jinfeng, Chen Cheng

Micro strain and stress field and the average field is significantly influenced by the interaction of inclusions of high volume fraction, and the composite mechanical properties changes a lot by the introduced inclusions. To reduce the error of using the theoretical model with single inclusion in real multi-inclusion-material property prediction, an inclusion interface cracking model is established based on the interaction direct derivative (IDD) estimate. Average e ective stress field is obtained under applied loading and residual stress based on the IDD estimate, then the stress intensity factor (SIF) of interface arc-crack around circular inclusion under the stress boundary condition is calculated. The critical applied stress is evaluated according to the e ective stress field and the interface arc-crack SIF, and the influence of inclusion elastic modulus, volume fraction, residual stress, and inclusion size are analysed. The result indicates that the method is e ective. Residual stress has remarkable influence to interface cracking; the critical applied stress is not monotonic and complicated with the inclusion sti ness variation when the residual stress is large, while the critical applied stress is increasing with the soft inclusion decreasing the sti ness and the sti inclusion increasing the sti ness when the residual stress is small; large size inclusion decreases the critical applied stress and detrimental to composite strength.

2016, 48(1): 154-162. doi: 10.6052/0459-1879-14-399

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LOCAL DYNAMICAL BEHAVIOR OF TWO-PARAMETER FAMILY NEAR THE NEIMARK-SACKER-PITCHFORK BIFURCATION POINT IN A VIBRO-IMPACT SYSTEM

Yue Yuan

A three-degree-of-freedom vibro-impact system with symmetry is considered. Due to the symmetry, the Poncar é map P is the second iteration of another virtual implicit map Q . It is shown that the symmetric period n-2 motion of the vibro-impact system corresponds to the symmetric fixed point of the Poncaré map. Then we can investigate bifurcations of the symmetric period n-2 motion by researching into bifurcations of the associated symmetric fixed point. Based on the symmetry of the system, it is shown that the Neimark-Saker-pitchfork bifurcation of the symmetric fixed point of the Poncaré map P corresponds to the Neimark-Saker-flip bifurcation of the map Q . By using the map Q , according to the two-parameter unfolding of the normal form, we reveal the possible local dynamical behaviors of the symmetric fixed point of the Poncaré map P near the Neimark-Saker-pitchfork bifurcation point in detail. Near this codimension two bifurcation point, the dynamic behaviors of the vibro-impact system can be expressed by a single symmetric fixed point, a pair of conjugate fixed points, a pair of conjugate quasi-periodic attractors or a single symmetric quasi-periodic attractor in the projected Poncaré section. The numerical simulation represents various possible cases near the Neimark- -Saker-pitchfork bifurcation point. It is shown that the interaction of the Neimark-Saker bifurcation and the pitchfork bifurcation may lead into the creation of some new results. The symmetric fixed point bifurcates into a pair of conjugate unstable fixed points firstly, and the two conjugate fixed points will bifurcate into the same symmetric quasi-periodic attractor finally.

2016, 48(1): 163-172. doi: 10.6052/0459-1879-15-144

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A HIGH-ORDER RIGID-FLEXIBLE COUPLING MODEL AND FREQUENCY VEERING OF A ROTATING CANTILEVER THIN PLATE

Fang Jianshi, Zhang Dingguo

The rigid-flexible coupling dynamics and frequency veering of a thin flexible plate on a rotating rigid body are further studied. The high-order coupling (HOC) dynamic model is derived by Lagrange's equations. The in-plane longitudinal shortening terms caused by lateral deformation, generally called non-linear coupling deformation terms, are considered here. Furthermore, all derived items associated with the non-linear coupling terms are retained completely in the HOC model. The HOC model can not only be applied in the small deformation case, but also in the large deformation case, and makes up the deficiency of the first-order approximation coupling (FOAC) model in the large deformation case. In addition, the frequency veering phenomena along with the corresponding mode shape variations are exhibited and discussed in detail. When two frequency loci veer, the nodal line patterns of the mode shapes switch their shapes each other, and the changes of the nodal line patterns are continuous in the mild veering region, while those in the abrupt veering region are discontinuous. The transitive frequency veerings among the multiple modes accompanied by mode shape transfer are also exhibited.

2016, 48(1): 173-180. doi: 10.6052/0459-1879-15-194

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THE NONLINEAR DYNAMIC BUCKLING ANALYSIS OF A THIN-WALLED CYLINDRICAL SHELL OF SUPERCAVITATING VEHICLES

Wang Jiefang, An Hai, An Weiguang

Dynamic buckling instability of the supercavitating vehicle has the characteristics of being hidden, sudden and dangerous. The researches of unstable region and instability amplitude are very important. The supercavitating vehicle was assumed as a thin-walled cylindrical shell with an axial periodic load. Considering the nonlinear geometric equation, physical equation and equilibrium equation, the nonlinear dynamic bulking differential equations were developed firstly, and then the nonlinear displacement expressions were given. After that, with the help of Galerkin variational method and Bolotin method, the dynamic bulking differential equation was transformed to Mathieu equation with periodic coefficients and nonlinear terms. At last, the nonlinear Mathieu equation was solved and the expressions of the stationary state vibration amplitude's in the 1st order and the 2nd order unstable region were got. The nonlinear parametric resonance curves of supercavitating vehicle were obtained, and the influences of the speed, load ration coefficient, load frequency of axial load and the vibration mode to the resonance were analyzed. The researches laid theoretical foundation for the dynamic buckling reliability analysis based on parametric resonance of a thin-walled cylindrical shell and dynamic optimum design based on parametric resonance reliability.

2016, 48(1): 181-191. doi: 10.6052/0459-1879-15-222

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NONLINEAR DYNAMICS DESIGN FOR PIECEWISE SMOOTH VIBRATION ISOLATION SYSTEM

Gao Xue, Chen Qian, Liu Xianbin

Piecewise smooth vibration isolation system is a class of nonlinear dynamics system with piecewise sti ness or damping, which can be found widely in vibration control engineering. This nonlinearity can achieve vibration isolation system's specified dynamics behaviour and improve its e ectiveness, but it will also bring some undesired nonlinear dynamics phenomena, such as amplitude sudden jump, period-doubling bifurcation, etc. The object of this paper is to study the design methodology for piecewise bilinear sti ness vibration system in the view of nonlinear dynamics. First, the entire picture of topology characteristic of frequency response for primary resonance is obtained through combining average method and singularity theory. Results show that the entire parameter plane is divided into four parts and the jump can be induced by both saddle-node and grazing bifurcation. Based on the results, the design principle of amplitude jump avoidance is presented. Then, the Poincaré map for periodic response in e ective isolation band is constructed, and the approach to avoid period-doubling bifurcation is given via eigenvalue analysis. It is verified that the stronger linear damping can suppress the period-doubling bifurcation. Last, this paper studies the e ect of noise on multi-steady state motion for piecewise smooth vibration isolation system. We find that the noise induces that the system's response transfer between the di erent steady states and it is adverse for vibration isolation.

2016, 48(1): 192-200. doi: 10.6052/0459-1879-15-099

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CONSTRAINT FORCE ALGORITHM FOR TREE-LIKE MULITBODY SYSTEM DYNAMICS

Liu Fei, Hu Quan, Zhang Jingrui

The e cient dynamics algorithm for multibody system has always been a research hotspot. In recent years, many e cient dynamics algorithms made progresses in improving the computational e ciency, but most of them cannot provide an explicit expression of the system's dynamics or resolve the constraint forces. Based on the above issue, a constraint force algorithm (CFA) and its serialized application for the dynamics modelling of an arbitrary multibody system in tree-topology are studied in this paper. The constraint forces for the system can be directly obtained by solving for the system motion through CFA. The presented algorithm is an extension of the original CFA which is only applicable to a single-chained system. It is obtained by analysing the dynamics and kinematics of an arbitrary node in a treelike system. Serialization of the algorithm is developed to reduce the computational cost to a linear relationship with the number of degrees of freedoms (DOFs). The accuracy of the proposed method is validated through a numerical simulation of a space robot with multiple manipulators. The e ciency of the serialized CFA is verified by comparing the CPU time of di erent algorithms.

2016, 48(1): 201-212. doi: 10.6052/0459-1879-15-201

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TRANSFER FUNCTION METHOD FOR ACOUSTIC PROPERTY STUDY OF UNDERWATER ANECHOIC LAYER

Ye Changzheng, Meng Han, Xin Fengxian, Lu Tianjian

This paper investigates theoretically the noise reduction property of a submarine wall structure consisting of submarine hull and underwater anechoic layers that contain inner holes. The case that both sides of the submarine wall structure are excited by fluids is considered. Built upon the transfer function method, an analytical anechoic model is developed to determine the pressure insertion loss induced by the anechoic layer. Numerical calculations are subsequently carried out to investigate the influence of fluid medium type, thickness of submarine hull, thickness of anechoic layer as well as shape of inner holes upon the vibro-acoustic properties of the structure. When the fluid medium inside is air, at low frequencies, the reduced vibration due to the anechoic layer is smaller than the increased vibration of submarine hull caused by the anechoic layer, and hence the vibration of the whole structure is increased; at high frequencies, however, the anechoic layer leads to significant attenuation in vibration of the whole structure. When the fluid inside is water, the anechoic layer attenuates the vibration of the whole structure at all frequencies, with the attenuation increasing with increasing frequency. Increasing the thickness of submarine hull or anechoic layer reduces the vibration of the whole structure. When the hole diameter first decreases and then increases in the direction from inside to outside the submarine, the anechoic layer exhibits the best attenuation e ect at high frequencies; when the hole diameter first increases and then decreases, the best attenuation is achieved at medium frequencies.

2016, 48(1): 213-224. doi: 10.6052/0459-1879-15-087

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NUMERICAL ANALYSIS OF HUMAN THORACIC INJURY RESPONSES IN VEHICLE LATERAL AND OBLIQUE CRASHES

Wang Fang, Yang Jikuang, Li Guibing, Zhou Shuiting, Han Yong, Li Fan

Vehicle lateral and oblique impacts account for a large proportion of traffic accidents resulting in serious occupant injuries. There is a lack of adequate investigations into the thoracic injury biomechanics in lateral and oblique impacts, compared to thoracic injuries in frontal impacts. Therefore, this article aims to study the biomechanical response and injury related parameters of the thorax under these two impact scenarios. First, an FE model of entire human body in sitting posture is established via combining previously developed FE models of the thorax, the head-neck and the lower extremities. Afterwards, the sitting human body FE model is used to simulate the 7 cadaver experiments by Shaw et al. in lateral and oblique impact to thorax. The calculated injury related response curves of the impact force, thorax deformation, and force-deformation are correspondingly within the biomechanical response curve corridors from experiments, which verified the validity of the sitting human body model. The peak value of impact force is close to the upper boundary of the test corridor, and the deformation approaches the lower boundary of the experimental results. Meanwhile, the peak of impact force from the lateral impact simulations is slightly larger than the resulting peak from oblique impact, and the peak of the timing is earlier. The peak of chest deformation in lateral impacts is smaller than that from the oblique impact, and the peak also appears earlier. This presents a trend consistent with the experimental results. Analysis shows that under the same intensity of impact load the thorax tolerance in lateral impact is higher than that in oblique impact. The thorax finite element model can accurately reproduce biomechanical response process in the lateral and oblique experiments. The model demonstrates good biofidelity to study the occupant thorax injury biomechanics.

2016, 48(1): 225-234. doi: 10.6052/0459-1879-15-265

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MECHANICAL ANALYSIS AND SIZING OPTIMIZATION OF OFFSHORE OIL SLICK TRACKING BUOY

Zhao Haifeng, Shi Jun, Wang Binbiny

O shore oil slick tracking buoy can be used to lock and locate oil trajectory when oil spill occurs. The adsorption capacity of oil-absorbing material inside buoy and the ocean winds has a great influence on positioning capability of buoy. The stronger adsorption capacity, the more closely integrated with oil and better positioned. First, from the analysis of oil- absorbing material stress, this paper measures the wind load of oil- absorbing material by using the principle of lever amplification in laboratory, and studies the variation trend of wind load along with disc diameter. The result is that wind load increases linearly along with increasing disc diameter. The study on adhesion of material along with increasing disc diameter indicates that adhesion has quadratic relations with the disc diameter. With the increase of disc diameter, the adhesion increases sharply. Second, studies suggest that adhesion should be composed of intermolecular force, surface tension and viscosity shear force. Intermolecular force is the main force, and surface tension and viscosity shear force is less than intermolecular forces from 1 to 2 orders of magnitude. Finally, based on the principle that adhesion force should be stronger than wind loads when buoy is working properly, the law of wind and adhesion force along with increasing disc diameter based on the experiment is extended to the large wind speed and large disc diameter. This paper studied the influence on changing diameter on force state of disc under bad sea conditions. The result is that the minimum disc diameter, adapted to the harsh sea conditions, is 38 cm.

2016, 48(1): 235-242. doi: 10.6052/0459-1879-15-147

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REVIEW OF NSFC PROJECTS ON MECHANICS DURING THE 2TH FIVE YEAR PLAN

Zhang Panfeng, Zhan Shige

The manuscript generally introduced the NSFC projects on mechanics during the 12th Five Year Plan. The project application and funding issues are presented, including the supporting institution ranking with a mount of proposals and their subordination distribution to the Chinese Academic of Science, the local provinces and autonomous regions, the Ministry of Education and the else ministries. Furthermore, the overview of project application and funding for General Programs, Young Scientists Fund, Fund for Less Developed Regions under di erent sub-discipline and research subject were given in details, accompanied with the statistics of age distribution, professional tile and the proportion of female for the applicants and principle investigators. At last, the suggestions about NSFC project findings were given to promote the development of mechanics.

2016, 48(1): 243-253. doi: 10.6052/0459-1879-16-001

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International and national academic activities organized or sponsored by CSTAM in 206

2016, 48(1): 254-261.

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2016 Vol. 48, No. 1

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