应用数学和力学

1992 Vol. 13, No. 2

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Chaotic Behaviour of the General Symbolic Dynamics

Fu Xin-chu, Chou Huan-wen

1992, 13(2): 103-109.

Abstract(1797) PDF(485)

Abstract:
This paper extends symbolic dynamics to general cases, Some chaotic properties and applications of the general symbolic dynamics(∑(X), σ) and its special cases are discussed, where X is a separable metric space.

A Numerical Calculation of Dynamic Buckling of a Thin Shallow Spherical Shell under Impact

Mu Jian-chun, Wu Wen-zhou, Yang Gui-tong

1992, 13(2): 111-119.

Abstract(1905) PDF(493)

Abstract:
Assuming the deformation of the shell has an axial symmetrically form,we transform the Marguerre's equations^[1] into difference equations, and use these equations to discuss the buckling of an elastic thin shallow spherical shell subjetted to impact loads.The result shows when impact load acts on the shell, a jump of the shell takes place dependent on the values λ and the critical buckling load increases with the enlargement of the loading area.

Fixed Points of Nonexpansive Mappings on Star-Shaped Subsets of a Convex Metric Space

Deng Lei, Ding Xie-ping

1992, 13(2): 121-127.

Abstract(1931) PDF(503)

Abstract:
In this paper,we give some characteristic properties of star-shaped sets which include a subset of a convex metric space.Using the characteristic properties,we discuss the ezistence problems of fized points of nonezpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an ezample which shows that our generalizations are essential.

A Second Order Uniform Difference Scheme for a Singularly Perturbed Turning Point Problem

Sun Xiao-di

1992, 13(2): 129-133.

Abstract(1746) PDF(546)

Abstract:
We construct a positive type diffcu(nce scheme for a singularly perturbed boundary value problem with a turning point, It's proved that this scheme is the second order convergence, uniformly in ε,to ihc solution of the singularly perturbed B. V. P.Numerical ezamples are provided.

On Singular Perturbation for a Nonlinear initial-Boundary Value Problem(Ⅱ)

Kang Lian-cheng

1992, 13(2): 135-143.

Abstract(2305) PDF(417)

Abstract:
In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary: When certain assumptions are satisfied and e is sufficiently small, the solution of this problem has a generalized asymptotic expansion(in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists.The layer exists in the neighborhood of t=0.This paper is the development of references [3-5].

Nonlinear Dynamic Response and Dynamic Buckling of Shallow Spherical Shells with Circular Hole

Fu Yi-ming, Liu Xiao-hu

1992, 13(2): 145-156.

Abstract(1813) PDF(475)

Abstract:
In this paper,the nonlinear equations of motion for shallow spherical shells with axisymmetric deformation including transverse shear are derived, The nonlinear static and dynamic response and dynamic buckling of shallow spherical shells with circular hole on elastically restrained edge are investigated.By using the orthogonal point collocation method for spaca and Newmark-β schmne for time,the displacement functions are separated and the nonlinear differential equations are replaced by linear algebraic equations to seek solutions.The numerical results are presented for different cases and compared with available data.

Fluid Mechanics of Microvascular Vasomotion and the Effects of Blood Viscoelasticity

Guo Zhong-san

1992, 13(2): 157-163.

Abstract(2044) PDF(798)

Abstract:
This paper deals witla blood flow caused by microvascular vasomotion with the focus on the effects of biood viscoelasticity on the pressure rise and wall resistance.It is shown that microvascular vasomotion plays a role of the "second heart" of the body which i.s of im portance in conveying blood, and that the effects of blood viscoelasticity greatly depend on the Weissenberg number and mean flow rate.

A Field Method for Integrating the Equations of Motion of Nonholonomic Controllable Systems

Mei Feng-xiang

1992, 13(2): 165-171.

Abstract(1777) PDF(514)

Abstract:
This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems.An example is given to illustrate the application of the method.

The Free-Interface Method of Component Mode Synthesis for Systems with Viscous Damping

Ni Zhen-hua, Huang Shang-heng, Wang Yi-cai

1992, 13(2): 173-180.

Abstract(2421) PDF(636)

Abstract:
This paper presents a new free-interface method of component mode synthesis for linear systems with arbitrary viscous damping.The left and right projection matrices described by state-variable vectors are first introduced for components with rigid-body freedom.The operator function of projection matrices for state displacement and state force is proved, and then the state residual flexibility matrix and the state residual inertia--relief attachment more are defined and employed. The results of three examples demonstrate that the method proposed in this paper leads to very accurate system eigenvalues and high mode-synthesis efficiency.

On the Approximate Computation of Extreme Eigenvalues and the Condition Number of Nonsingular Matrices

Lei Quang-yao

1992, 13(2): 181-186.

Abstract(2033) PDF(542)

Abstract:
From the formulas of the conjugate gradient, a similarity between a symmetric positive definite(SPD) matrix A and a tridiagonal matrix B is obtained.The elements of the matrix B are determined by the parameters of the conjugate gradient.The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B.The approximation of extreme eigenvalues of A can be obtained as a ‘by-product' in the computation of the conjugate gradient if a computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient.If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on A^TA.Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.

Asymptotic Solutions of Mathieu Equation with Damping

Tao Ming-de

1992, 13(2): 187-191.

Abstract(2089) PDF(400)

Abstract:
This paper first reduces the motion equation of a collapsible tube to the Mathieu equation with damping.Then the stability charts correcting the accuracy to each order are obtained with the method of asymptotic expansions.The accuracy of the results obtained with the average variational method is shown, And some phenomena observed in the experiment are also explained.

1992, 13(2): 192-192.

Abstract(1721) PDF(394)

Abstract: