应用数学和力学

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(2368) 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 these conclusions,the principle for choosing the mesh size and the number of truncated terms in the fundamental solution are given.It isshown that the theoretical ana analysis in this paper are consistent with thenumerical results in [1].

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

Xu Jiachu, Liu Renhuai

1998, 19(2): 105-112.

Abstract(2613) 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 amplitude of vibration is obtained by Galerkin's method.Finally,the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period to linear period for nonlinear free vibration of the plate.

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

Bi Qinsheng, Chen Yushu, Wu Zhiqiang

1998, 19(2): 113-120.

Abstract(2901) 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 chaos are studied in this paper.

Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation

Cheng Fude

1998, 19(2): 121-125.

Abstract(2483) 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,and the their stability and location isdetermined.

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

Li Gangchang, He Shiben

1998, 19(2): 126-135.

Abstract(2642) 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 and dissipative systems,and a new expression is made to the relation between asymptotic stability for the manifold of equilibrium positions of this class of nonholonomic systems and dissipative forces.Two examples are finally given to illustrate the application of the theorems.

Plane Problems in Piezoelectric Media with Elliptic Inclusion

Hou Mishall, Yang Qijun

1998, 19(2): 136-144.

Abstract(2212) 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 displacement in inclusion are all constant.In addition,the electromechanical behavior of piezoelectric influence at the elliptic rim of the infinite matrix with only acting mechanical or electric load is discussed with numerical examplex.

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(2459) 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 integral equation of the second kind which is solved numerically.

The Auto-Adjustable Damping Method for Solving Nonlinear Equations

Chang Haiping, Huang Taiping

1998, 19(2): 151-155.

Abstract(2199) 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 numerical instability.It can not fulfill the engineering requiements.Newton's method and its variants can not settle this problem.As a result,the application of numerical sinulation for the strongly nonlinear problems is limited.An auto-adjustable damping method has been presentd in this paper.This is a further improvement of Newton's method with damping factor A set of vector of damping factor is introduced.This set of vector can be adjsted continuously during the iterative process in accordance with the judgement and adjustment.An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process.Then.the numerical stability will be ensured for the solution of complicated strongly nonlinear equations.Using this method.some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully.It can be used for the numerical simulation ofstrongly nonlinear problems in engineering such as nonlinear hydrodynamic and aerodynamics,heat transfer and struactural dynamic response etc.

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

Zhang Yingshi, Wang Xieshan

1998, 19(2): 156-164.

Abstract(2431) 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:forced responses of such plates under different-type loads are discussed with generalized functions.

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(2112) 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" of complex model of poly-order arediscussed.The results indicate that "semi-rupture" applears for some models on specific condition the blown-up appears during the whole evolution.For fluid however,the weadly-nonlinear model is of more artificiality and there is much room for arguing about the smoothing scheme of the numerical integral on the basis of continuous thinking and so on.

1998 Vol. 19, No. 2