应用数学和力学

1998 Vol. 19, No. 2

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Boundary Element Method for Solving Dynamical Response of Viscoelastic Thin Plate(Ⅱ)——Theoretical Analysis

Ding Rui, Zhu Zhengyou, Cheng Changjun

1998, 19(2): 95-103.

Abstract(2339) PDF(689)

Abstract:
In this paper,the necessary theoretical analysis for the approximation boundary element method to solve dynamical response of viscoelastic thin plate presented in [1] is.discussed.The theorem of existence and uniqueness of the approximate solution andthe error estimation are also obtained.Based on t...

Shear Effects on Large Amplitude Forced Vibration of Symmetrically Laminated Rectilinearly Orthotropic Circular Plates

Xu Jiachu, Liu Renhuai

1998, 19(2): 105-112.

Abstract(2587) PDF(510)

Abstract:
In this paper,nonlinear forced vibration of symmetrically laminated rectilined rectilinearly orthotropic circular plates excited by a harmonic force q₀cosωt including effects of transverse shear deformation is discussed.The ahalytical solution for the relationship between forcing frequency and ampli...

Bifurcation in a Nonlinear Duffing System with Multi-Frequency External Periodic Forces

Bi Qinsheng, Chen Yushu, Wu Zhiqiang

1998, 19(2): 113-120.

Abstract(2876) PDF(787)

Abstract:
By introducing nonlinear frequency,using Floquel theory and referring to the characteristics of the solution when it passes through the transition bounaries all kinds of bifurcation modes and their transition boundaries of Duffing equation with two periodic excitatins as well as the possible ways to...

Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation

Cheng Fude

1998, 19(2): 121-125.

Abstract(2461) PDF(693)

Abstract:
In this paper,foe Melnikov function method has been used to analyse the distance between stable manifold and unstable manifold of the soft spring Duffing equation^[1] after its heteroclinic orbits rupture as the result of a small perturbation.The conditionsthat limit circles are bifurcated are given,...

Lagrange’s Theorem for a Class of Nonholonomic Systems and Its Application

Li Gangchang, He Shiben

1998, 19(2): 126-135.

Abstract(2606) PDF(582)

Abstract:
The stability problem for the manifold of equilibrium positions of a class of nonholonomic systems is studied is studied in this paper.Based on Liapunov's direct method and the definition of stability,Lagrange's theorem of holonomic systems is extended to a class of nonholonomic conservative systems...

Plane Problems in Piezoelectric Media with Elliptic Inclusion

Hou Mishall, Yang Qijun

1998, 19(2): 136-144.

Abstract(2182) PDF(639)

Abstract:
This paper expresses potential function of complex variable in Fabere series and the solution in closed form is provided for the plane stress problems in piezoelectric media with elliptic inchusion.It is shown from the solution that the stress,strain,electric field intensity and electric displacemen...

Using Fredholm Integral Equation of the Second Kind to Solve the Vertical Vibration of Elastic Plate on an Elastic Half Space

Jin Bo

1998, 19(2): 145-150.

Abstract(2435) PDF(638)

Abstract:
The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition.By applying Abel transformation the dual integral equations are reduced to Fredholm inte...

The Auto-Adjustable Damping Method for Solving Nonlinear Equations

Chang Haiping, Huang Taiping

1998, 19(2): 151-155.

Abstract(2179) PDF(1323)

Abstract:
The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures,then executing the numerical simulation.For the strongly nonlinear problems,the solution obtained in the iterative prpcess is always difficult,even divergent due to the nume...

Vibrations of One-Way Rectangular Stepped Thin Plates on Winkler’s Foundation

Zhang Yingshi, Wang Xieshan

1998, 19(2): 156-164.

Abstract(2406) PDF(605)

Abstract:
Differential equations of free forced vibrations of one-way rectangular stepped thin plated on Winkler's foundation are established by using singular functions,their general solutions are solved:exprssion of vibration mode function and frequency equations on usual supports are derived from Woperator...

The “Rebel Travelling” of General Nonlinear Evolutional Equation and Discussion on Related Problems

Ouyang Shoucheng, Wang Yongzong, Wu Yong, Li Chao

1998, 19(2): 165-173.

Abstract(2084) PDF(724)

Abstract:
This paper is a part of series works for diseussing the "auto-destruction effects" of general nonlinear evolutional equations.The blown-up of Navier-Stockes equation isdiscussed in references [1,2].Some expansion is made in this paper,and the blown-upof ordere-1 or 2 models and the "rebel travelling...