应用数学和力学

Quasi-Green’s Function Method for Free Vibration of Clamped Thin Plates on Winkler Foundation

LI Shan-qing, YUAN Hong

2011, 32(3): 253-262. doi: 10.3879/j.issn.1000-0887.2011.03.001

Abstract(1885) PDF(731)

Abstract:

The quasi-Green's function method was employed to solve the free vibration problem of clamped thin plates on Winkler foundation.A quasi-Green's function was established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates on Winkler foundation was reduced to Fredholm integral equations of the second kind by Green formula.Irregularity of the kernel of integral equation was overcome by choosing a suitable form of the normalized boundary equation.Numerical results show high accuracy of the method given by the present paper,and it is an effective mathematical method.

Aerodynamic Unstable Critical Wind Velocity for Three-Dimensional Open Cable-Membrane Structures

WEI De-min, ZHU Mei-ling, LI Di

2011, 32(3): 263-270. doi: 10.3879/j.issn.1000-0887.2011.03.002

Abstract(1519) PDF(860)

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

Bifurcation of Rupturing Path by the Nonlinear Damping Force

Zainal Abdul Aziz, Dennis Ling Chuan Ching, Faisal Salah Yousif

2011, 32(3): 271-278. doi: 10.3879/j.issn.1000-0887.2011.03.003

Abstract(1548) PDF(238)

Abstract:
The linear damping mechanism of Rayleigh waves was extended for the nonlinearity.Conferring to the model,analytical method was chosen for the solutions.These solutions depict the unusual bifurcation of the rupturing path related to the intersection point of antisoliton and soliton.

Buckling of Embedded Microtubules in Elastic Medium

Muhammad Taj, ZHANG Jun-qian

2011, 32(3): 279-285. doi: 10.3879/j.issn.1000-0887.2011.03.004

Abstract(1483) PDF(641)

Abstract:
Motivated by the application of Winkler-like model for buckling analysis of embedded carbon nanotubes,an orthotropic Winkler-like model was developed to study buckling behavior of embedded cytoskeletal microtubules within cytoplasm.Experimental observations of buckling of embedded cytoskeletal microtubules reveal that embedded microtubules bear a large compressive force as compared to free microtubules.Our theoretical model predicts that embedded microtubules in elastic medium bear large compressive forces than free microtubules.The estimated critical pressure is found not only in good agreement with the experimental values of pressure-induced buckling of microtubules[Needleman D J,Ojeda-Lopez M A,Kai Ewert U R,Miller H P,Wilson L,Safiny C R.Biophys J,2005,89(5):3410-3423; Needleman D J,Ojeda-Lopez M A,Raviv U,Ewert K,Jones J B,Miller H P L,Wilso L,Safinya C R.Phys Rev Lett,2004,93(19):1981041-1981044.].But also,due to mechanical coupling of microtubules with surrounding elastic medium,critical buckling force has increased considerably,which well explains the theory that mechanical coupling of microtubules with the elastic medium increases compressive forces that microtubules can sustain[Brangwynne C P,MacKintosh F C,Kumar S,Geisse N A,Talbot J,Mahadevan L,Parker K K,Ingber D E,Weitz D A.The Journal of Cell Biology,2006,173 (5):733-741] suggesting that the present model is a good approximation for buckling analysis of embedded microtubules.

Stability Analysis of Radial Inflation of Incompressible Composite Rubber Tubes

YUAN Xue-gang, ZHANG Wen-zheng, ZHANG Hong-wu, ZHU Zheng-you

2011, 32(3): 286-292. doi: 10.3879/j.issn.1000-0887.2011.03.005

Abstract(1507) PDF(826)

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

Scattering of SH-Waves on the Isosceles Triangular Hill Joined by Semi-Cylindrical Canyon

HAN Feng, WANG Guang-zheng, KANG Chao-yang

2011, 32(3): 293-311. doi: 10.3879/j.issn.1000-0887.2011.03.006

Abstract(1953) PDF(720)

Abstract:
Scattering of SH-wave on the triangular hill joined by semi-cylindrical canyon in half-space was studied with the methods of complex function and moving coordinates.The studied model was divided into two domains at first,and the wave functions,which satisfy the required condition at each wedge,are constructed in each equation,which was solved by Fourier expanding.Finally,numerical examples and relative 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): 312-323. doi: 10.3879/j.issn.1000-0887.2011.03.007

Abstract(1587) PDF(656)

Abstract:
The effect of rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half space was presented using the mechanics of the medium as derived by Cowin and Nunziato.The velocity equation was derived and the results were discussed.It is observed that there may be two torsional surface wave fronts in the medium whereas there exists three wave fronts of torsional surface waves in the absence of rigid boundary plane given by Dey et al(Tamkang Journal of Science and Engineering,2003,6(4):241-249.).The results also reveals that in the porous layer,the Love wave is also available along with the torsional surface waves.It is remarkable that phase speed of Love wave in a porous layer with 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 frequency of oscillation increases.

Numerical Method for Optimum Motion of Undulatory Swimming Plate in Fluid Flow

QIAN Qin-jian, SUN De-jun

2011, 32(3): 324-332. doi: 10.3879/j.issn.1000-0887.2011.03.008

Abstract(1579) PDF(877)

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

Shock Calculation Based on Second Viscosity Using Localized Differential Quadrature Method

ZHAO Yong, ZONG Zhi, LI Zhang-rui

2011, 32(3): 333-343. doi: 10.3879/j.issn.1000-0887.2011.03.009

Abstract(1586) PDF(726)

Abstract:
Based on the second viscosity,localized differential quadrature (LDQ) method was applied to solve shock tube problems.Firstly,the necessity was explained to consider the second viscosity to calculate shocks,then shock tubes based on the viscosity model were simulated,and finally,the roles of shear viscous stress and the second viscous stress were checked.The results show that the viscosity model combined with LDQ method can capture the main characters of shock and have the advantages of objectivity and simplicity.

Axisymmetric Magnetohydrodynamic flow of a Micropolar Fluid Between Unsteady Stretching Surfaces

T. Hayat, M. Nawaz, S. Obaidat

2011, 32(3): 344-356. doi: 10.3879/j.issn.1000-0887.2011.03.010

Abstract(1449) PDF(685)

Abstract:
This investigation examines the time dependent MHD flow problem of a micropolar fluid between two radially stretching sheets.Both the cases (n=0,0.5) of strong and weak concentrations of microelements are taken into account.Suitable transformations were employed for the conversion of partial differential equations into the ordinary differential equations.The solutions of the resulting problems were developed by a homotopy analysis method (HAM).Angular velocity,skin friction coefficient and wall couple stress coefficient were illustrated for various parameters of interest.

Large Scall High Performance Computation on 3D Explosion and Shock Problems

FEI Guang-lei, MA Tian-bao, HAO Li

2011, 32(3): 357-364. doi: 10.3879/j.issn.1000-0887.2011.03.011

Abstract(1531) PDF(686)

Abstract:
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 was used.The dynamic parallel program was designed based on the generally used MPI model.The numerical test of dynamic parallel program agrees well with that of the original parallel program,also agrees with actual situation.

Chebyshev Finite Spectral Method With Extended Moving Grids

ZHAN Jie-min, LI Yok-sheung, DONG Zhi

2011, 32(3): 365-374. doi: 10.3879/j.issn.1000-0887.2011.03.012

Abstract(1738) PDF(724)

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

2011 Vol. 32, No. 3