应用数学和力学

Electromechanical Waves in Ceramics——Numerical Simulation

Gerard A. MAUGIN, Bemard COLLET, Joël POUGET

1985, 6(12): 1043-1052.

Abstract(1835) PDF(475)

Abstract:
A simple one-dimensional model is used to simulate numerically the propagation of linear and nonlinear waves in a deformable ceramic. The nummrical scheme used provides the response in stress or strain and electric field within the sample and the voltage at a resistive external circuit connecting the two faces of the sample. Space-time diagrams of the propagation are obtained for various mechanical loads. The voltage response obtained agrees well with experimental results in the linear regime. In the nonlinear one, the steepening of the electromechanical wave yielding a shock wave is exhibited.

Equi-Strength Design for Statically Indeterminate Beams

X. Tang, Ye Kai-yuan

1985, 6(12): 1053-1059.

Abstract(2122) PDF(672)

Abstract:
In this paper a method for equi-strength design of statically indeterminate beams is presented, based on the principle of minimum complementary energy. And an analytical expression is derived for the stiffness variation of single or multi-span beams under the application of arbitrarily distributed loads, concentrated forces and couples. Illustrated examples concerning beams with fixed width are riabbe height or sandwich beams with variable thickness of outer sheets are also given. The comparison with reported results shows the effectiveness of the proposed method.

Dynamical Equations for Treeshaped Multi-Rigid-Body Systems

Wang En-song

1985, 6(12): 1061-1070.

Abstract(2203) PDF(619)

Abstract:
In this paper, the "Configuration Graph" for a treeshaped system is brought, which presents the position and the arrangement of an arbitrary number of interconnected rigid bodies. By means of "Configuration Matrix" this paper analyses the motion of treeshaped multi-rigid-body systems and derives their dynamical equations while it is not necessary to bring out such ideas as "Augmented-Body" and "Subsystem". In such dynamical equations, dynamical parameters of a treeshaped multi-rigid-body is closely associated with its configuration matrix.

Application of the Finite Part of a Divergent Integral in the Theory of Elasticity

Wang Min-zhong

1985, 6(12): 1071-1078.

Abstract(2047) PDF(829)

Abstract:
Using the finite part of a divergent integral, we transform Kelvin's solutions, Boussinesq's solutions and Mindlin's solutions in the three-dimensional theory of elasticity into corresponding solutions in the two-dimensional theory. Besides, its application in plane problems is also given.

The Relaxational Oscillation Solution for Fitzhugh’s Nerve Conduction Equation

Lin Chang, Li Ji-bin, Liu Zeng-rong

1985, 6(12): 1079-1086.

Abstract(2144) PDF(551)

Abstract:
By using the matching asymptotic method, we calculated the analytic expression of relaxational osillation sochition for Fitznugr's nerve conduction equation, oscillation period and the parametric region in which the relaxational oscillation occurs.

Higher Order Theory Across a Three-Dimensional Axially-Symmetrical Curved Shock Near the Stagnation Point

Zhu Yue-rui, Yao Zhao-kang

1985, 6(12): 1087-1099.

Abstract(2180) PDF(706)

Abstract:
The next order conditions across a three-dimensional curved shock near stagnation point have been established, including the effects of heat conduction, viscosity and the shock structure. These shock conditions involve the local shock curvature in addition to its local inclination. Explicit results have been obtained for the correctional formulations in the mass flux across the shock, the stagnation enthalpy, the tangential component of velocity and the normal component of momentum flux.

Equations of Motion of Variable Mass in High-Order Non-Holonomic Mechanical System

Zhao Guan-kang, Zhao Yue-yu

1985, 6(12): 1101-1109.

Abstract(2069) PDF(636)

Abstract:
The paper establishes the universal D'Alembert's principle in variable mass mechanical system. Then derives the different kinds of the differential equations of variable mass in high-order non-holonomic mechanical system.Finally, the applications for example are illustrated by these new equations.

The Boundary Element Method (BEM) for Wave Equation

Gu Wei-hua

1985, 6(12): 1111-1120.

Abstract(2169) PDF(561)

Abstract:
The formula of BEM suited to solve the problems of wave propagation in boundless medium is obtained from numerical treatment of Kirchhoff integral equation. After quoting the coefficients of refraction and reflection of wave at surface or interface, the expression of BEM which is suitable for the problems of wave propagation in multi-isotropic mediums is also given.

The Equilibrium State of a Flexible Pendulum

Wang Mao-hua

1985, 6(12): 1121-1122.

Abstract(1783) PDF(587)

Abstract:
In this paper the analytical solutions of the equilibrium states of a flexible pendulum with oscillating base motions are given.

1985 Vol. 6, No. 12