应用数学和力学

1997 Vol. 18, No. 10

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Dynamical Equations of Various Types for Finite Deformable Polar Elastic Media

Dai Tianmin

1997, 18(10): 861-865.

Abstract(2178) PDF(547)

Abstract:
In the present paper,some additional new defmitions on the kinematics and dynamics are introduced,and the dynamical equations of Boussinesq type,Kirchhoff type,Signorini type and Nowzilov type for finite deformable polar elaslic media are systematically derived from the consideration of Euler angles as angular coordinated and the dynamical equations of Cauchy type presented by Dluzewski.

Hydrodynamic Interaction between Two Vertical Cylinders in Water Waves

Zhou Xianchu, Wang Dongjiao, Allen T. Chwang

1997, 18(10): 867-878.

Abstract(2053) PDF(574)

Abstract:
The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory.One of the two cylinders is fixed at lhe bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave.Both the diffracted wave and the rediation wave are studied in the present paper.A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem.The wave-excited forces and moments on the cylinders,the added masses and the radiation damping coeffcients of the oscillating cylinder are all expressed explicitly in series form.The coeffcients of the series are determined by solving algebraic equations.Several numerical examples are given to illustrate the effects of various parameters,such as the separation distance,the relative size of the cylinders,and the incident angle,on the first-order and steady second-order forces,the added masses and radiation-damping coefficients as well as the response of theoscillating cylinder.

Convex-Model Analysis of the Seismic Response

He Caiying, Zhang Jinghui

1997, 18(10): 879-884.

Abstract(1995) PDF(515)

Abstract:
In ellipsoidal Fourier-bound convex model(EFB model) is proposed in the present paper to express the uncertainty of seismic excitation,and several methods of selecting parameters of the model are explained.An analytical expression is obtained for the worst response of the sigle-degree-of-freedom(SDOF) system with the EFB model.A numerical simulation shows that the traditionol prediction of maximum response can yield the value substantially lower than that predicted by the EFB model.This means that lhe traditional designing method bosed on standard seismic inputsmay lead to unsafe desikn decisions.

Two-Dimensional Electroelastic Fundamental Solutions for General Anisotropic Piezoelectric Media

Liu Jinxi, Wang Biao, Du Shanyi

1997, 18(10): 885-891.

Abstract(2067) PDF(528)

Abstract:
Explicit foniulas for 2-D electroelastic fundamental solutions in general anisotropic piezoelectric media subjected to a line force and a line charge are obtained by using the plane wave decomposition method and a subsequent application of the resiue calculus."Anisotropic" means thal any material symmetry restrictions are not assumed "Two dimensional" includes not only in-plane problems.but also anti-plane problems and problems in which in-plane and anti-plane deformations couple each other.As a special case,the solutions.for transversely isotropic piezoelectric media are given.

Strongly oblique Interactions between Internal Solitary Waves with the Same Mode

Zhu Yong

1997, 18(10): 893-898.

Abstract(2231) PDF(456)

Abstract:
In this paper,by using the Lagrangian coordinates,the strongly oblique interactions between solitary waves with Ihe same mode in a Stratified fluid are discussed,which includes the shallow fluid case and deep.fluid case.It is.found that the interactions are described by the KP equation for the shallow fluid case,the two dimensional intermediate long wave equation(2D-LW equation) for the deep fluid case and the two-dimensional BO equation(2D-BO equation)for the infinite deep fluid case.

The Classical Pressure Vessel Problem for Void Damage Materials

Fu Mingfu, Sheng Dongfa, Li Xianglin

1997, 18(10): 899-904.

Abstract(1865) PDF(524)

Abstract:
In this paper,the classical pressure vessel problem for void damage materials is studied from the theory of mncrostructure in linear elasticity.The solutions are quasi static.The Stress distribution is predicted by isotropic linear elasticity.The displacement and damage fields exhibit a volumetric viscoelasticity induced by considering material damage.

On the Problem of the Number of Bifurcation Solutions at Singular Point

Zhou Kun

1997, 18(10): 905-909.

Abstract(2154) PDF(460)

Abstract:
In this paper,it is proved that the solutions of a nonlinear equation are isolated under Ihe condition that the singular points are isolated.It shows that there musl have and Only have finite solutions branching from bifurcation point.This is important.for the numerical analysis of bifurcation problems.

Modification in the Theory on Flexural-Torsional Buckling of Structures

E Guokang

1997, 18(10): 911-920.

Abstract(2694) PDF(505)

Abstract:
In this paper,the problems existing in the present theory on flexural-torsional buckling of structures are discussed,and the buckling procedure is found to be restricted to certain development order of doplacements and rotations by the present theory.A fresh idea is.therefore,proposedfor the mathematical description of actual flexural-torsional buckling procedure of structures.New geometric equations are formulated and a set of new potential variational equation and neutral equilibrium equations are got for the flexural-torsional buckling analysis of structures.Examples are given to detect the numerical diffrence between the modified theory and the present accepted theory.

Fourth-Order Accurate Difference Method for the Singular Perturbation Problem

Liu Chuanhan

1997, 18(10): 921-929.

Abstract(2530) PDF(538)

Abstract:
In this paper,the numerical solution of fourth-order ordinary differential equations is considered.To approximate the differential equation,the Hermitian scheme on a special nonequidistant mesh is used.The fourth order convergence uniform in the perturbation parameter is proved.The numerical result shows the pomtwise convergence,too.

On Force-Free Magnetic Fields and Beltrami Flows

Feng Qingzeng

1997, 18(10): 931-936.

Abstract(1981) PDF(464)

Abstract:
Solenoidal vector fields,which satisfy the condition that the field vector every where parallels to its curl,have complex topologicla structures,andusually show chaotic behaviors.In this paper,analytical solutions for vector fields with constant proportional facfor in three basic coordinate sysems are presented and it is pointed out that a Beltrami flow can sustain a steady force-free magnetic fild in a perfectly conducting fluid,provided the magnetic field is parallel to the velocity everywhere.

Remarks on Nonlinear Galerkin Method for Kuramoto-Sivashinsky Equation

Wu Yujiang

1997, 18(10): 937-945.

Abstract(1967) PDF(465)

Abstract:
This paper is concentrated on a nonlinear Galerkin method with s_m small-scale components for Kuramoto-Sivashmsky equation,in which convergence results and the analysis of error estimates are given.The conclusion shows that this choce of modes is efficient for The method modifred.

Nonlinear Stability of Truncated Shallow Spherical Shell with Variable Thickness under Uniformly Distributed Load

Yan Shengping

1997, 18(10): 947-952.

Abstract(1933) PDF(578)

Abstract:
In this paper,to begin with.the nonlinear differential equations of a truncaled shallow spherical shell with variable thickness under uniformal distributed load are linearized by step-by-step loading method.The linear differential equations can be solved by spline collocanon method.Critical loads have been obtained accordingly.

The Research of Longtime Dynamic Behavior in Weakly Damped Forced KdV Equation

Tian Lixin, Xu Zhenyuan

1997, 18(10): 953-958.

Abstract(2397) PDF(569)

Abstract:
It is presented that there exists approximate inertial manifolds in weakly damped forced Kdv equation with with periodic boundary conditionsIIbns.The approximate inertial manifolds provide approximant of the attractror by finite dimensional smooth manifolds which are exphcitly defined And the concepl leads to new numerical schemes which are well adapted to the longtime behavior of dynamical system.