应用数学和力学

1993 Vol. 14, No. 10

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The Solution of Dynamic Point-Ring-Couple in an Elastic Space and Its Properties

Yun Tian-quan, Gu He-ning

1993, 14(10): 845-852.

Abstract(2190) PDF(650)

Abstract:
The solution of dynamic Point-Ring-Couple at the origin, on z=0 plane, in an elastic space is presented and its properties are discussed. Let shocking loads be uniformly distributed, along the direction of circumference, at a circle, on z=0 plane, with radius a and centered at the origin. Then, the solution of our problem is obtained via integral calculation for a→0. When the intensity of this dynamic Point-Ring-Couple is varied with sincot, the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis, become zero stressed surfaces at any time instance. The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sinωt is found.

The Solution of Integral Equations with Strongly Singular Kernels Applied to the Torsion of Cracked Circular Cylinder

Li Yu-lan, Ma Zhi-qing, Tang Ren-ji

1993, 14(10): 853-859.

Abstract(2160) PDF(527)

Abstract:
In this paper, the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions. The torsion problem of cracked circular cylinder is reduced to solving a system of integral equations with strongly singular kernels. Using the numerical method of these equations, the torsional rigidities and the stress intensity factors are calculated to solve the torsion problem of circular cylinder with star-type and other different types of cracks. The numerical results are satisfactory.

Integral Theory for the Dynamics of Nonlinear Nonholonomic System in Noninertial Reference Frames

Luo Shao-kai

1993, 14(10): 861-871.

Abstract(2166) PDF(657)

Abstract:
This paper establishes the integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frame. Firstly, based on the Routh equation of the relative motion of nonlinear nonholonomic system gives the first integral of the system. Secondly, by using cyclic integral or energy integral reduces the order of the equation and obtains generalized Routh equation and Whittaker equation respectively. Thirdly, derives canonical equation and variation equation and by using the first integral constructs integral invariant. And then, establishes the basic integral variants and the integral invariant of Poincare-Cartan type. Finally, we give a series of deductions.

The Activation Method for Discretized Conservative Nonlinear Stability Problems with Multiple Parameter and State Variables

Deng Chang-gen

1993, 14(10): 873-881.

Abstract(2321) PDF(555)

Abstract:
For nonlinear stability problems of discretized conservative systems with multiple parameter variables and multiple state variables, the activation method is put forward, by which activated potential functions and activated equilibrium equations are derived. The activation method is the improvement and enhancement of Liapunov-Schmidt method in elastic stability theory. It is more generalized and more normalized than conventional perturbation methods. The activated potential functions may be transformed into normalized catastrophe potential functions. The activated equilibrium equations may be treated as bifurcation equations. The researches in this paper will motivate the combination of elastic stability theory with catastrophe theory and bifurcation theory.

Singular Perturbation Solutions of the Nonlinear Stability of a Truncated Shallow Spherical Shell under Linear Distributed Loads along the Interior Edge

Kang Sheng-liang

1993, 14(10): 883-894.

Abstract(2376) PDF(608)

Abstract:
Using a singular perturbation method, the nonlinear stability of a truncated shallow, spherical shell without a nondeformable rigid body at the center under linear distributed loads along the interior edge is investigated in this paper. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained.

Gauss White Noise Perturbations of Nonholonomic Mechanical Systems

Shen Ze-chun, Liu Feng-li

1993, 14(10): 895-902.

Abstract(2168) PDF(554)

Abstract:
The perturbations of nonholonomic mechanical systems under the Gauss white noises are studied in this paper. It is proved that the differential equations of the first-order moments of the solution process coincide with the corresponding equations in the non-perturbational case, and that there are ε²-terms but no ε-terms in the differential equations of the second-order moments. Two propositions are obtained. Finally, an example is given to illustrate the application of the results.

Application of the Modified Method of Multiple Scales to Solving the Problem of a Thin Clamped Circular Plate a Very Large Deflection

Qiao Zong-chun

1993, 14(10): 903-912.

Abstract(1929) PDF(534)

Abstract:
In this paper, asymptotic behaviour of the solution to the problem of a thin damped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in [1-2]. The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in [3]. However, by contrast, the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in [3]. It is also shown that the restriction of the method of paper [1-2] pointed out in paper [4] is not essential, and several computation errors in [3] are corrected as well.

The Problem of Parametric Integration to the Slip Line Field in the Compression of Thick Workpiece

Zhao De-wen, Zhang Wei-jun

1993, 14(10): 913-918.

Abstract(2209) PDF(639)

Abstract:
An integration depending on a parameter to the compression of a thick workpiece has been obtained. For the conventional prevailing numerical formula a definite functional relationship bet-ween φ and y is found. Therefore a parametric integration can be used to get an analytical solution. Take the slip line field for l/h=0.121 as an example, the analytical solution is basically the same as the prevailing numerical one. It is justified theoretically that for the slip line field a parametric integration is perfectly possible for a satisfactory analytical solution.

On CML Model for Study of Spatiotemporal Chaos

Huang Xin, Liu Zeng-rong, Xie Hui-min

1993, 14(10): 919-928.

Abstract(1855) PDF(523)

Abstract:
A new coupled map lattic (CML) model is given by using some stability analysis for the related difference equations. Numerical results show that the new model is an effective one of studying spatiotemporal chaos, especially for strongly coupled systems.

Stability of the Burgers Shock Wave

Lü Xian-qing

1993, 14(10): 929-930.

Abstract(1973) PDF(516)

Abstract:
This paper considers the stability of the Burgers shock wave solution with respect to infinitesimal disturbance. It is found that the Burgers shock wave is asymptotically stable in the Liapunov sense.

Dynamic Response and Reliability Analysis of Random Structures

Can Hong, Li Qiu-sheng, Li Zhi-yan

1993, 14(10): 931-938.

Abstract(1782) PDF(615)

Abstract:
The finite element method determining dynamic response of random structures subjected to random dynamic load is studied, the formulas for dynamic response of random structures and reliability based on random resistibility are proposed in this paper.