力学学报

2013, 45(1): 1-1. doi: 10.6052/0459-1879-2013-1-20130101

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STUDY ON THE NON-SMOOTH MECHANICAL MODELS AND DYNAMICS FOR SPACE DEPLOYABLE MECHANISMS

Cao Dengqing, Chu Shiming, Li Zhengfa, Liu Rongqiang

The space deployable mechanism is widely used to develop and support the flexible solar array and payloads including parabolic antenna, plane phased array radar, and synthetic aperture radar in the aerospace engineering field. Non-smooth characteristics and the corresponding dynamic phenomena play a very important role in the design of space deployable mechanism. This paper reviews the state-of-art of non-smooth mechanical modeling and nonlinear dynamics for the space deployable mechanisms. First of all, the non-smooth properties such as the contact impact forces and friction models are elaborated for hinges with clearances. Then, the dynamical modeling methods, analytical approach, and parametric design are systematically presented for the mechanisms with clearances. Moreover, the nonlinear dynamic phenomena such as harmonic resonance, existence and stability of periodic motions, and various kinds of bifurcations are presented for the space deployable mechanisms whose joints are with clearances. Finally, directions for further works on the dynamics, stability and control for the non-smooth dynamical system of space deployable mechanisms are proposed.

2013, 45(1): 3-15. doi: 10.6052/0459-1879-12-341

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STUDY ON RESPONSE CHARACTERISTICS OF A CLASS OF PIECEWISE SMOOTH NONLINEAR PLANAR MOTION SYSTEMS

Jiang Jun, Gao Wenhui

In this paper, the response characteristics of a two-degree-of-freedom non-autonomous piecewise smooth nonlinear system, which consists of linear and nonlinear subsystem, are investigated. The piecewise smooth system can be used to determine the most important responses of a rotor/stator rubbing systems, and possesses some following peculiar features: (1) the switching surface is defined by the two displacement coordinates of the system and is a magnitude surface in the state space; (2) the touch of the periodic solutions of subsystems with the switching surface occurs always simultaneously at all points of the solution to make it different from gazing bifurcations or phenomena in the usual nonsmooth systems; (3) there is no periodic solution formed through connection of trajectories from two subsystems. So some techniques developed for the bifurcation analysis of equilibriums or periodic solutions are not directly applicable to the system. Thus, according to the dynamical characteristics of subsystems, this paper tries to classify the parameter regions into the switching sensitive and insensitive regions. In this way, the responses of whole system in the switching insensitive regions can be obtained from the analysis of the responses of subsystems. For some responses of the whole systems in the switching sensitive regions, explanation is given for their occurrence based on the dynamical characteristics of subsystems.

2013, 45(1): 16-24. doi: 10.6052/0459-1879-12-342

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BORDER-COLLISION BIFURCATION IN A KIND OF NON-SMOOTH MAPS

Qin Zhiying, Li Qunhong

For a kind of piecewise map, its nonsmoothness with the parameter z is discussed, and the conditions for border-collision bifurcation and smooth flip/fold bifurcation are derived. These bifurcation conditions are verified by numerical simulation, and the period-adding bifurcation scenario is a general phenomenon for non-smooth maps. The bifurcation scenario is rooted on the interrelation between border-collision bifurcation and smooth flip/fold bifurcation. The parameter z has important effect on the bifurcation scenario, but the parameter has a minor effect, so the analysis γ on bifurcation scenarios with parameters can be simplified by giving γ=0.

2013, 45(1): 25-29. doi: 10.6052/0459-1879-12-317

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GRAZING-INDUCED CHAOSTIC CRISIS FOR PERIODIC ORBITS IN VIBRO-IMPACT SYSTEMS

Feng Jinqian, Xu Wei

A numerical approximation of grazing manifold is proposed via the digraph cell mapping method. The global dynamics of grazing-induced crisis for a typical Du ng vibro-impact system are then investigated. The results reveal that, the singularity caused by the grazing nature of periodic orbits can induce a bifurcation where a periodic saddle and a chaotic saddle arise simultaneously. When the stable and unstable manifolds of the periodic saddle undergo the tangency, a boundary crisis occurs and a chaotic attractor is then brought from the chaotic saddle. Also, grazing phenomenon of periodic orbits induced by noise can be observed. This grazing phenomenon can induce a novel interior crisis, where a chaotic attractor arises due to the collision of this periodic attractor and the chaotic saddle.

2013, 45(1): 30-36. doi: 10.6052/0459-1879-12-315

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THEORETICAL ANALYSIS AND EXPERIMETNAL VERIFICATION FOR PAINLEV碋 PARADOX

Zhao Zhen, Liu Caishany, Chen Bin

Painlevé paradox may appear in multi-rigid-body systems subjected to Coulomb’ friction. No solution or multiple solutions make the systems inconsistent or indeterminate. It is worth investigating how the subsequent motions of the systems in inconsistent states evolve since the actual systems will always move on. The theoretical analysis and the experimental verification are carried out to confirm the tangential impact in the inconsistent case of the systems. The characteristic of the stick motions are confirmed during tangential impact.

2013, 45(1): 37-44. doi: 10.6052/0459-1879-12-316

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RESEARCH PROGRESS ON THE EXPERIMENTAL MEASUREMENT METHODS OF MECHANICAL PROPERTIES OF THERMAL BARRIER COATINGS

Zhu Jianguo, Xie Huimin, Liu Zhanwei

Thermal barrier coatings (TBCs) are widely used in turbine blades of aeronautics, astronautics and nuclear reactors for the purpose of insulation from hot gas stream and protection of metallic substrate. However, the gas-turbine engines are under the threat of premature TBCs failures, such as fracture and spallation during service. The experimental measurement methods of mechanical properties of TBCs have become the major tasks. The research progresses of TBCs are reviewed, including the origins of misfit stresses leading to TBCs failure, the experimental measurement methods and systems on mechanical properties of TBCs, the thermography technique for the non-destructive detecting of interfacial spallation of TBCs, the life prediction of TBCs and the shortages in the current researches as well as future development of TBCs.

2013, 45(1): 45-60. doi: 10.6052/0459-1879-12-080

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DIRECT NUMERICAL SIMULATION OF THE INTERACTION OF 2D SHOCKWAVE AND SHEAR LAYER

Liu Xuliang, Zhang Shuhai

Direct numerical simulation (DNS) of the interaction of shock wave and shear layer was performed. The compressible unsteady two-dimensional Navier-Stokes equations were solved using the fifth-order WENO scheme combined with the third-order TVD Runge-Kutta scheme. The purpose of this paper is to reveal the mechanism of sound generation in the interaction of shock wave and shear layer. The results show that: (1) When incident shock wave is passing through the shear layer, the center of the vortex cores is shifted towards the lower side; (2) The interaction of incident shock wave and shear layer generates shocklet, and then acoustic wave is generated and radiated at the locus of contact of shocklet and shear layer; (3) Several arc-shocks are formed after reflected shock wave passing through shear layer; (4) When reflected shock wave is passing through shear layer, shock wave is leaking in the braid region and shock-associated noise is generated at the saddle points between vortices. This is a form of shock leakage mechanism.

2013, 45(1): 61-75. doi: 10.6052/0459-1879-12-106

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STUDY ON THE UNSTEADY VERTICAL CAVITY OF THE EXIT-WATER CAVITOR

Chen Weiqi, Wang Baoshou, Yan Kai, Yi Shuqun

The unsteady vertical cavity produced by the underwater cavitator moving rapidly towards the water surface is investigated theoretically. The mathematical model of the unsteady vertical cavity under water is presented; the formula of the vertical cavity length influenced by the gravity and water surface is derived, and the life span of cavity shedding from exit-water cavitator is also obtained from the formula. For the underwater body with cavitator, the acting position in the body of the high-pressure produced by the collapsed cavity is also calculated by the formula; moreover, the condition and criterion of keeping the underwater body from collapse high-pressure is presented.

2013, 45(1): 76-82. doi: 10.6052/0459-1879-12-164

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THE CONVECTION-DISPERSION EQUATION AND THE MECHANISM OF SUSPENSION IN TURBULENT OPEN-CHANNELS

Zhang Lei, Zhong Deyu, Wu Baosheng, Liu Lei

The suspended sediment usually occupies a large portion of the total load transported by streams in large fluvial rivers. Therefore, it is of crucial importance to study the mechanism involved in the suspension of suspended sediment. In this paper, we derive an equation for suspended sediment transportation and the sediment diffusion coeffcient based on the two-fluid model by introducing the concept of dispersion velocity, and apply the theory to calculate the concentration profiles of uniform two-dimensional open channel flows. Comparisons with the experimental data from Einstein and Chien and classical diffusion models are also presented, which show that present theory agrees well with the experimental data. In addition, we analyze the variations of influences of different effects contributing to the suspended sediment in the vertical direction. It is found that the suspension of the sediment in open channels is the result of three different actions, which are the turbulence diffusion of mixture, particle turbulence, and particle collisional stress. The result also shows that it is insu cient to ascribe the sediment in suspension solely to the turbulence of the flow.

2013, 45(1): 83-93. doi: 10.6052/0459-1879-12-146

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STRESS INTENSITY FACTOR FORMULAS FOR DCDC AND SCDC SPECIMENS

Ni Min, Gou Xiaoping, Wang Qizhi

In the paper, the confusions about the different stress intensity factor formulas in the foreign references for the double cleavage drilled compression (DCDC) specimens are clarified theoretically and numerically. It is proved that the formulas for DCDC obtained by Plaisted et al. using a modified solution for a pair of short cracks at the opposite edges of a circular hole in an infinite plate subjected to compression, and using an Euler-Bernoulli beam solution for a long crack, respectively, are both inadequate, with errors existing either in the formulation or in the model-based principle. A new formula of stress intensity factor for DCDC is obtained by fitting the wide-ranging numerical results of finite element analysis; the maximum error of the new formula is less than 7%. The new formula is also simpler in form than that given by Jenne et al., and with larger applicable range as compared to the formulas of He et al. for both the dimensionless crack length and the dimensionless plate width. Furthermore, for the newly proposed single cleavage drilled compression (SCDC) specimens, a stress intensity factor formula for SCDC is also formulated, and the maximum error of the formula for SCDC is less than 5%. The two formulas derived in this paper can be used for testing mode-I fracture toughness of brittle materials using either the DCDC or the SCDC specimens.

2013, 45(1): 94-102. doi: 10.6052/0459-1879-12-179

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AN EVIDENCE-THEORY-BASED RELIABILITY ANALYSIS METHOD FOR UNCERTAIN STRUCTURES

Jiang Chao, Zhang Zhe, Han Xu, Bai Yingchun

A new reliability analysis technique based on evidence theory that can effciently reduce the computational cost is developed for uncertain structures. In this method, a design optimization is introduced to obtain the non-probability index and a design point, and an assistant area is constructed. Through the assistant area, it can markedly reduce the number of focal elements with extreme analysis. Moreover, the computation number of the limit-state function decreases with the help of interval analysis method. Numerical examples and engineering problems are used to demonstrate the effectiveness of the proposed method.

2013, 45(1): 103-115. doi: 10.6052/0459-1879-12-040

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RESEARCH OF DYNAMIC EXPERIMENTAL MODELING FOR NONLINEAR STRUCTURE UNDER PARAMETRIC AND FORCED EXCITATION

Zhu Chenzhong, Ye Min

Incremental harmonic balance nonlinearity identification (IHBNID) method has already been applied to the experimental modeling method for single-degree-of-freedom dynamical equation and shows reasonable match between numerical simulation and experimental system. This paper aims to apply the IHBNID to multi-degree-of-freedom nonlinear parametric and forced excitation vibration system. So the experimental platform of L-shape beam system is set up and the dynamical equation of the beam is built with the experimental modeling method and the IHBNID. The result of numerical simulation shows fairly good compatibility with experimental system on qualitative and quantitative aspects. This theory including experimental modeling method and the IHBNID demonstrates that it also can be applied to experimental systems with variable frequencies and motions, such as the period-doubling motion.

2013, 45(1): 116-128. doi: 10.6052/0459-1879-12-174

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THE ENERGY RELEASE RATE OF CRACKED HYPERELASTIC BODY UNDER ARBITRARY LOADINGS

Zhang Zuoqi, Liu Bin

Energy release rate is an important parameter characterizing fracture behaviors of materials. In classic fracture mechanics, only formulae for the energy release rate of linear elastic cracked structures are given by compliance method, especially limited to fixed loading or displacement boundary conditions. Moreover, the fracture toughness and toughening mechanism of hyperelastic materials such as biomaterials and polymer (rubber-like materials) are attracting more and more attention of researchers. The paper aims to develop general formulae to calculate the energy release rate of nonlinear elastic structures under arbitrary loading conditions, and these formulae also facilitate to evaluate the stability of crack growth. During the deducing process, several important but misleading concepts are further clarified.

2013, 45(1): 129-133. doi: 10.6052/0459-1879-12-137

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A NOVEL ENRICHED FUNCTION OF ELEMENTS CONTAINING CRACK TIP FOR FRACTURE ANALYSIS IN XFEM

Jiang Shouyan, Du Chengbin

In the paper, a novel enriched function for those elements containing crack tip is proposed. By the method of trigonometric transform, the four crack tip enriched functions in the standard extended finite element methods (XFEM) are reduced to the two ones. The reduced enriched functions still keep the two properties, such as the stress singular at the crack tip and the discontinuities of crack surfaces. The enriched degrees of freedom for those nodes of element containing crack tip is thereby reduced from 8 to 4. The two orthogonal level set functions are used to represent the existing crack in materials. The method for identifying the enriched type of elements is described in details. An integration schemes for enriched elements are given. Finally, several classic fracture problems are given to verify the numerical precision of the proposed crack tip enriched functions. The results show the effectiveness of the proposed method.

2013, 45(1): 134-138. doi: 10.6052/0459-1879-12-144

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A NEW METHOD FOR FREE VIBRATION ANALYSIS OF COMPOSITE LAMINATED SHELLES OF REVOLUTION

Qu Yegao, Hua Hongxing, Chen Yong, Long Xinhua, Meng Guang

A semi-analytical domain decomposition approach is proposed for free vibration analysis of laminated composite shells of revolution subjected to arbitrary boundary conditions. A laminated shell structure is divided into some shell segments along the axis of revolution. The geometrical boundaries are treated as special interfaces as those between two adjacent shell segments. All interface continuity constraints are incorporated into the system potential functional by means of a subdomain generalized variational principle and least-squares weighted residual method. Double mixed series, i.e. the Fourier series and Chebyshev orthogonal polynomials, are adopted as assumed admissible displacement functions for each shell segment. In order to validate the proposed formulation, typical laminated shells of revolution, such as circular cylindrical, conical and spherical shells, with various combinations of edge support conditions, are examined. The numerical results obtained from the present method show good agreement with previously published results. The present solution is very effcient, robust and accurate. The computational advantage of the approach can be exploited to gather useful and rapid information about the effects of geometry and boundary conditions on the vibrations of laminated composite shells of revolution.

2013, 45(1): 139-143. doi: 10.6052/0459-1879-12-078

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BULLETIN OF THE SUPPORT BY NATIONAL NATURAL SCIENCE FOUNDATION OF CHINA AND SYMPOSIUM OF INDEPENDENT COMPUTATIONAL MECHANICS SOFTWARES

Ning Jianguo, Ma Tianbao, Zhan Shige, Zhang Panfeng

2013, 45(1): 144-148. doi: 10.6052/0459-1879-13-009

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