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2011年 第32卷 第3期    刊出日期：2011-02-28

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Articles

Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation

李善倾 袁鸿

2011, 32(3):  265-276.  doi:10.1007/s10483-011-1412-x

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The quasi-Green’s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green’s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of the problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green’s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.

Aerodynamic unstable critical wind velocity for three-dimensional open cable-membrane structures

魏德敏 朱美玲 李頔

2011, 32(3):  277-284.  doi:10.1007/s10483-011-1413-9

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The aerodynamic unstable critical wind velocity for three-dimensional open cable-membrane structures is investigated. The geometric nonlinearity is introduced into the dynamic equilibrium equations of structures. The disturbances on the structural surface caused by the air flow are simulated by a vortex layer with infinite thickness in the structures. The unsteady Bernoulli equation and the circulation theorem are applied in order to express the aerodynamic pressure as the function of the vortex density. The vortex density is then obtained with the vortex lattice method considering the coupling boundary condition. From the analytical expressions of the unstable critical wind velocities, numerical results and some useful conclusions are obtained. It is found that the initial curvature of open cable-membrane structures has clear influence on the critical wind velocities of the structures.

Bifurcation of rupture path by nonlinear damping force

A. A. ZAINAL C. C. D. LING S. Y. FAISAL

2011, 32(3):  285-292.  doi:10.1007/s10483-011-1414-9

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The linear damping mechanism of the Rayleigh waves is extended to the nonlinear one. Conferring to the model, the analytical method is chosen for the solutions. These solutions depict the unusual bifurcation of the rupture path related to the intersection point of antisoliton and soliton.

Buckling of embedded microtubules in elastic medium

M. TAJ 张俊乾

2011, 32(3):  293-300.  doi:10.1007/s10483-011-1415-x

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Motivated by the application of Winkler-like models for the buckling analysis of embedded carbon nanotubes, an orthotropic Winkler-like model is developed to study the buckling behavior of embedded cytoskeletal microtubules within the cytoplasm. Experimental observations of the buckling of embedded cytoskeletal microtubules reveal that embedded microtubules bear a large compressive force as compared with free microtubules. The present theoretical model predicts that embedded microtubules in an elastic medium bear large compressive forces than free microtubules. The estimated critical pressure is in good agreement with the experimental values of the pressure-induced buckling of microtubules. Moreover, due to the mechanical coupling of microtubules with the surrounding elastic medium, the critical buckling force is increased considerably, which well explains the theory that the mechanical coupling of microtubules with an elastic medium increases compressive forces that microtubules can sustain. The model presented in the paper is a good approximation for the buckling analysis of embedded microtubules.

Stability analysis of radial inflation of incompressible composite rubber tubes

袁学刚 张文正 张洪武 朱正佑

2011, 32(3):  301-308.  doi:10.1007/s10483-011-1416-8

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The inflation mechanism is examined for a composite cylindrical tube composed of two incompressible rubber materials, and the inner surface of the tube is subjected to a suddenly applied radial pressure. The mathematical model of the problem is formulated, and the corresponding governing equation is reduced to a second-order ordinary differential equation by means of the incompressible condition of the material, the boundary conditions, and the continuity conditions of the radial displacement and the radial stress of the cylindrical tube. Moreover, the first integral of the equation is obtained. The qualitative analyses of static inflation and dynamic inflation of the tube are presented. Particularly, the effects of material parameters, structure parameters, and the radial pressure on radial inflation and nonlinearly periodic oscillation of the tube are discussed by combining numerical examples.

Scattering of SH-waves on triangular hill joined by semi-cylindrical canyon

韩峰 王光政 康朝阳

2011, 32(3):  309-326.  doi:10.1007/s10483-011-1417-7

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Scattering of SH-waves on the triangular hill joined by semi-cylindrical canyon in half-space is studied using the method of complex function and moving coordinates. The model being studied is divided into two domains. The wave functions satisfying the required condition at each wedge are constructed in each equation. The equations are solved with Fourier expansion. Numerical results are provided to discuss the influence of scattering of SH-waves.

Effect of rigid boundary on propagation of torsional surface waves in porous elastic layer

S. GUPTA A. CHATTOPADHYAY D. K. MAJHI

2011, 32(3):  327-338.  doi:10.1007/s10483-011-1418-6

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The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato (Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13(2), 125–147 (1983)). The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. (Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6(4), 241–249 (2003)). The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.

Numerical method for optimum motion of undulatory swimming plate in fluid flow

钱勤建 孙德军

2011, 32(3):  339-348.  doi:10.1007/s10483-011-1419-x

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A numerical method for the optimum motion of an undulatory swimming plate is presented. The optimum problem is stated as minimizing the power input under the condition of fixed thrust. The problem is singular for the invisible modes, and therefore the commonly used Lagrange multiplier method cannot predict an optimum solution but just a saddle point. To eliminate the singularity, an additional amplitude inequality constraint is added to the problem. A numerical optimization code with a sequential quadratic programming method is used to solve the problem. The method is applied to several cases of the motion of two-dimensional and three-dimensional undulatory plates, and the optimum results are obtained.

Shock calculation based on second viscosity using local differential quadrature method

赵勇 宗智 李章锐

2011, 32(3):  349-360.  doi:10.1007/s10483-011-1420-6

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Based on the second viscosity, the local differential quadrature (LDQ) method is applied to solve shock tube problems. It is shown that it is necessary to consider the second viscosity to calculate shocks and to simulate shock tubes based on the viscosity model. The roles of the shear viscous stress and the second viscous stress are checked. The results show that the viscosity model combined with the LDQ method can capture the main characteristics of shocks, and this technique is objective and simple.

论文

Axisymmetric magnetohydrodynamic flow of micropolar fluid between unsteady stretching surfaces

T. HAYAT M.NAWAZ S.OBAIDAT

2011, 32(3):  361-374.  doi:10.1007/s10483-011-1421-8

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This investigation examines the time dependent magnetohydrodynamic (MHD) flow problem of a micropolar fluid between two radially stretching sheets. Both strong and weak concentrations of microelements are taken into account. Suitable transformations are employed for the conversion of partial differential equations into ordinary differential equations. Solutions to the resulting problems are developed with a homotopy analysis method (HAM). The angular velocity, skin friction coefficient, and wall couple stress coefficient are illustrated for various parameters.

Articles

Large-scale high performance computation on 3D explosion and shock problems

费广磊 马天宝 郝莉

2011, 32(3):  375-382.  doi:10.1007/s10483-011-1422-7

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Explosion and shock often involve large deformation, interface treatment between multi-material, and strong discontinuity. The Eulerian method has advantages for solving these problems. In parallel computation of the Eulerian method, the physical quantities of the computaional cells do not change before the disturbance reaches to these cells. Computational efficiency is low when using fixed partition because of load imbalance. To solve this problem, a dynamic parallel method in which the computation domain expands with disturbance is used. The dynamic parallel program is designed based on the generally used message passing interface model. The numerical test of dynamic parallel program agrees well with that of the original parallel program, also agrees with the actual situation.

Chebyshev finite spectral method with extended moving grids

詹杰民 李毓湘 董志

2011, 32(3):  383-392.  doi:10.1007/s10483-011-1423-6

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A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for the wave surface, and the other type is for highly variable gradients. The method has high-order accuracy because of the use of the Chebyshev polynomial as the basis function. The polynomial is used to interpolate the values between the two non-uniform meshes from a previous time step to the current time step. To attain high accuracy in the time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme is used. To avoid numerical oscillations caused by the dispersion term in the Korteweg-de Vries (KdV) equation, a numerical technique on non-uniform meshes is introduced. The proposed numerical scheme is validated by the applications to the Burgers equation (nonlinear convectiondiffusion problems) and the KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparisons. Numerical results agree very well with the corresponding analytical solutions in all cases.