应用数学和力学

1988 Vol. 9, No. 12

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Spin and Rotation Velocity of the Stretching Frame in Continuum

Guo Zhong-heng

1988, 9(12): 1045-1048.

Abstract(1684) PDF(608)

Abstract:
The present paper investigates the conceptual root of the current incorrect mechanical interpretation of the spin in continuum and gives the correct one.

Normal Perforation of a Thin Infinite Plate by a Flat Headed Cylindrical Projectile

Hsueh Dah-wei

1988, 9(12): 1049-1054.

Abstract(1873) PDF(490)

Abstract:
Analytical formulae for calculating the stress acting on the contact surface between projectile and target and for calculating the moving velocity of this contact surface under impact are both suggested in this paper. These formulae can be thought of as a generalization of the well-known Hopkins and Kolsky's theory in plastic domain. And then, an analytical formula for calculating ballistic limit is also suggested. It is also proved in this paper that the shear stress acting on the cylindrical surface of the plug is distributed uniformly.

Meinikov Function and Poincaré Map

Xu Zhen-yuan, Li Li

1988, 9(12): 1055-1063.

Abstract(2143) PDF(427)

Abstract:
In this paper we give the relationship between Melnikov function and Poincare map, and a new proof for Melnikov's method. The advantage of our paper is to give a more explicit solution and to make Melnikov function for the subharmonics bifurcation and Melnikoy function which the stable manifolds and unstable manifolds intersect transversely into a formula.

Singularly Perturbed Phenomena of Semilinear Second Order Systems

Lin Zong-chi, Lin Su-rong

1988, 9(12): 1065-1072.

Abstract(1724) PDF(434)

Abstract:
In this paper we consider singular perturbed phenomena of semilinear second ordersystems, under appropriate assumptions, the existence and asymptotic behavior as ε→0⁺ of solution of vector boundary value problem are proved by constructing specialinvariant regions in which solutions display so-called boundary layer phenomena andangular layer phenomena.

The Expression of Free Energy for Thermoelastic Material and Its Relation to the Variable Material Coefficients

Wang Hong-gang

1988, 9(12): 1073-1078.

Abstract(1898) PDF(455)

Abstract:
The expression of free energy is expanded in a power series, in which there aren't any terms of order higher than third in the temperature increments θ^* and second in the strains γ_ij in this paper. The regular patterns of the material coefficients changing with temperature increments can be derived from this expression. These regulations accord with the experimental graph in references but the constants in the expression of free energy must be determined by experimental data.It is pointed out that the variable modulus of elasticity E and shearing modulus of elasticity G are independent of each other, but the rest of the coefficients are related to them.

Space Variable Transform Method for Free Vibration Analysis of Thick Cylindrical Shelf with Arbitrary Boundary Conditions

Ni Hai-ying, Weng Zhi-yuan

1988, 9(12): 1079-1085.

Abstract(1878) PDF(533)

Abstract:
In this paper, a general analytical method-space variable transform method is presented fur solving free vibration problems of thick cylindrical shell with arbitrary boundary conditions. Free vibration characteristics of cantilever thick cylindrical shell are evaluated by the presented method, and the numerical results are compared with the corresponding results of thin shell theory and experimental values. Theoretical analysis and calculating results show that the method presented in this paper has good convergence and accuracy and can be extended to analyze free vibration of beams, plates and shells.

Analysis of Nonlinear Large Deformation Problems by Boundary Element Method

Xie He-ping

1988, 9(12): 1087-1096.

Abstract(1666) PDF(532)

Abstract:
In this paper, the author deduces an approximate solution of nonlinear influence function in rate form for two-dimensional elastic problems on current configuration by the method of comoving coordinate system.Here BEM formulation of large deformation based on Chen's theory^[1] is given. The computational processes of nonlinear boundary integral equation is discussed. The author also compiles a nonlinear computing program NBEM. Numerical examples show that the results presented here is available to the solution of engineering problems.

Series Soution for Elastic Behavior of Corrugted Circular Plates in Large Deflection under Arbitrary Loads

Lu Yun-yun, Wang Xiu-xi, Huang Mao-guang

1988, 9(12): 1097-1108.

Abstract(1676) PDF(576)

Abstract:
Chebyshev polynomials are used to solve the problem of large deflection for corrugated circular plates with a plane central region under arbitrary loads based on the nonlinear bending theory of anisotropic circular plates. Numerical results are compared with those available in the literature. The present method shows higher accuracies and larger application ranges.

Some Problems of Second Method of Lyapunov in Discrete Systems

Li Zhong, Huang Lin

1988, 9(12): 1109-1115.

Abstract(1941) PDF(447)

Abstract:
The geometric properties of the solution set of Lyapunov equation of linear time-invariant discrete system are discussed. Furthermore,the stabitility of piecewise linear discrete systems is studied and some sufficient conditions are obtained for the asymptotical stability of piecewise linear discrete systems in which each sub-system is stable. The results are applied to second order piecewise linear systems.

The Convergent Condition and United Formula of Step Reduction Method

Ji Zhen-yi

1988, 9(12): 1117-1127.

Abstract(1844) PDF(503)

Abstract:
The step reduction method was first suggested by Prof. Yeh Kai-yuan^[1]. This method has more advantages than other numerical methods. By this method, the analytic expression of solution can he obtained for solving nonuniform elastic mechanics. At the same time, its calculating lime is very short and convergent speed very fast. In this paper, the convergent condition and united formula of step reduction method are given by mathematical method. It is proved that the solution of displacement and stress resultants obtained by this method can converge to exact solution uniformly, when the convergent condition is satisfied. By united formula, the analytic solution can be expressed as matrix form, and therefore the former complicated expression can be avoided. Two numerical examples are given at the end of this paper which indicate that, by the theory in this paper, a right model can be obtained for step reduction method.

Periodic Solution and Chaotic Behavior of a Class of Nonautonomic Pendulum Systems with Large Damping

Sun Jian-hua

1988, 9(12): 1129-1137.

Abstract(1728) PDF(464)

Abstract:
In this paper the existence and uniqueness of the periodic solution is studied for a class of second order nonautonomic pendulum systems and the parameter regions tor which the system in chaos is myestigated when φ(t)=1-ελcosωt,F(t)=β+εμ(cosωt-ωsinωt) and the tamping coefficient a>0 is large. The result obtained generalize the corresponding conclusions of papers [1-8].