应用数学和力学

1994 Vol. 15, No. 9

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A Comparison of Four Recent Numerical Schemes Giving High Resolution of Shock Wave and Concentrated Vortex

Huang Dun, Yang Chun

1994, 15(9): 759-765.

Abstract(1769) PDF(515)

Abstract:
In recent ten years high resolution difference schenies for the computation of thefull unsteady Eulerian system of equations for invisid compressible gas finds celebratedprogress.This paper tests furtherly,by a complex two-dimensional unsteady problem,four recent schemes.to them attentions are paid.The test problem is the initial stageof a two-dimensional diffraction and reflection of a plane shock wave,impinging on arectangular obstacle.At whose top side there are two sharp corners,near which flow.parameters finds severe variation.There is occurrence of expansion fan with a centerand also concentrated vortices.To simulate them well,the schemes should have goodadaptivity.The special shock Mach number M_s=2.068 is so chosen,that at this M_s,the partical velocity behind impinging shock in fixed coordinate system is just equal tothe speed of sound there,this condition also occurs along a curve in the region ofexpansion fan with a center at the corner.This can clarify the computational featureof different schemes in case,when one of the eigenvalues is just zero.Zero eigenvaluemay spoil some schemes locally.Graphical visualization of the computational resultsmay,show features of the tested schemes about the shock wave resolution,schemeviscosity,expansion wave and the ability.to simulate the process of the generation ofunsteadv concentrated vortex.

Generalized Variational Principles of Symmetrical Elasticity Problem of Large Deformation

Zhao Yu-xiang, Gu Xiang-zhen, Li Huan-qiu

1994, 15(9): 767-774.

Abstract(1935) PDF(984)

Abstract:
This paper is based on the geometrical nonlinear theories of deformation presented by Chen Zhi-da^[1],Lagrange's multiplier mothod is used to study the symmetry elasticity problems of large deformation.The general rariational priieiplesof potential energy and complemenlary energy,and the general variation principle of dynamic problem have been proved.In the meantme it is also proved that the general vatiaton principles of potential energy and complementary energy are equivalent.

On the Inverse Problem in Calculus of Variations

Liang Li-fu, Shi Zhi-fei

1994, 15(9): 775-788.

Abstract(2104) PDF(833)

Abstract:
The inverse problem in calculus of variation is studied.By introducing a newconcept called Varialional Integral,a new method to systematically study the inverse problem in calculus of rariations is given.Using this new method to the elastodynamics and hydrodynamics of viscous fhuids some kinds of variaiional principles and generalized variational prineiples are obtained respectively.

Free Bending Vibration of Annular Cylindrical Tank Partially Filled With Liquid in the Consideration of Surface Wave

Zhou Ding

1994, 15(9): 789-797.

Abstract(2017) PDF(466)

Abstract:
This paper studies the problem of free bending vibration of annular cylindricaltank partially filled with liquid in the consideration of surface wave.The exactformulae of the mode shape functions and frequencies are deduced.Results can beobtained by means of computer.The analysis shows that the effect of liquid on vibration of annular cylindrical tank is equivalent to different generalized distributivemasses attached to inner and outer cylinders respectively.

Finite Element Analysis for the Unsteady Nearshore Circulation Due to Wave-Current Interaction(Ⅱ) Two-Step Explicit Finite Element Method

Wu Wei-xiong

1994, 15(9): 799-806.

Abstract(1647) PDF(450)

Abstract:
In this paper,the two-step explicit finite element analysis for the numerical model of the unsteady nearshore circulation proposed in Rart(Ⅰ)and its realization of Fortran program are presented.A circulation has been clearly shown in the calculated wave-current velocity field,and it is in good agreement with observations.

An Anayntical Solution of the Second-Order Wave Force on a Vertical Circular Cylinder

Zhou Zhi-li, Dai Yi-shan

1994, 15(9): 807-819.

Abstract(1596) PDF(579)

Abstract:
An analytical solution of second-order diffractidn potential for a vertical circular cylinder of large diameter is presented in this paper.The problem of second-order radiation condition is discussed and it is concluded that the circum ferential components of the second-order potential have to satisfy the Sommcrfeld radiation condition.By using the mathematical formulas derived in this paper,the inhomogeneos terms of second-order free surface boundary condition are expressed in such a way that the particular solution of the second-order potential can be easily written out.The ezact expression of the second-order wave force given in this method is simple and easy to be caculated pumericully.Numerical results are also compared with expevimental values.

Stability of the Navier-Stokes Equation(Ⅰ)

Shi Wei-hui

1994, 15(9): 821-822.

Abstract(1581) PDF(536)

Abstract:
In this paper we give an example of non-uniqueness of local solution for somekinds of boundary value problem of Navier-Stokes equation.

Oscillation Theorems of Higher Order Nonlinear Delay Differential Equations

Jin Ming-zhong

1994, 15(9): 823-830.

Abstract(1832) PDF(511)

Abstract:
This paper has given necessary and sufficient conditions for oscillation of a classof higher order nonlinear delay differential equations,and given some sufficientconditions or necessary conditions for oscillation of a forced delay differential equation.

Hoether's Conservation Laws of Holonomic Nonconservative Dynamical Systems in Generalized Mechanics

Qiao Yong-fen, Yue Qing-wen, Dong Yong-an

1994, 15(9): 831-837.

Abstract(2183) PDF(713)

Abstract:
In the present paper,three kinds of forms for Noether's conservation laws of hol-onomic nonconservative dynamical systems in generalized mechanics are given.

Stability of the Korteweg-de Vries Solitary Wave Solution

Lü Xian-qing

1994, 15(9): 839-840.

Abstract(1622) PDF(404)

Abstract:
This paper considers the stabilily of the Korteweg-de Vries solitary wave solutionwith respect to infinitesmal dislurbance.It is found that the Korteweg-de Vries solitarywave solulion is unstable in the Liapunov sense.

Analysis of the Eccentric Cylindrical Thin Shell

Chang Ming, Chang Li-li

1994, 15(9): 841-848.

Abstract(1547) PDF(424)

Abstract:
The present paper gives the approximate equations of the eccentric cylindrical thin shell under small deflections.By means of the analytical method,we solved the equations.Thus the relations between the stress,the displacement and the eccentricity of the eccentric cylindrical thin shell are obtained.