应用数学和力学

1993 Vol. 14, No. 5

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The Chaotic Behavior of a Nonlinear Oscillator

Pei Qin-yuan, Li Li

1993, 14(5): 377-387.

Abstract(1864) PDF(575)

Abstract:
Behavior of bifurcation and chaos in a forced oscillator =fcosωτ containing a square nonlinear term is investigated by using Mel nikov method and digital computer simulations.

The Fundamental Methods of Dynamical Analysis of the Blast-Resistant Underground Structures

Zhao Yu-xiang, Song Xi-tai, Qian Er-xuan

1993, 14(5): 389-396.

Abstract(1807) PDF(492)

Abstract:
In this paper, the generalized variational principle of dynamic analysis for the blast-resistant underground structures is established, and the corresponding generalized functional of elastoplastic analysis for underground structures is derived, and the generalized variational principle of nonconservative system is given, thus the fundamental of dynamical analysis for underground structures to resist blast is proposed. Finally, for the underground cylindrical structure to resist blast, dynamical calculations are made, and compared with the test results.

The Generalized Variational Principles in Applications for Nonlinear Structural Analysis

Cheng Xiang-sheng

1993, 14(5): 397-406.

Abstract(1826) PDF(554)

Abstract:
This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of σ=βε^1/m or τ=Cγ^1/m, namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.

Supplementary Study on Anisotropic Plastic Stress Fields at a Stationary Plane-Stress Crack-Tip(Ⅰ)

Lin Bai-song

1993, 14(5): 407-414.

Abstract(1901) PDF(448)

Abstract:
The results in ref. [1] are not suitable for the cases of α≥2, For this reason, we use the method in ref. [1] to derive the general expressions of the anisotropic plastic stress fields at a stationary plane-stress crack-tip for both of the cases of α=2 and α>2. As an example, we give the analytical expressions of the anisotropic plastic stress fields at the stationary tips of mode Ⅰ and mode Ⅱ plane-stress cracks for the case of α=2.

An Approximate Analytical Solution of the Cylindrical Detonation Wave Generated by the Linear Explosion

Yuan Yi-wu

1993, 14(5): 415-418.

Abstract(1964) PDF(542)

Abstract:
The solution of the cylindrical detonation wave generated by the linear explosion was obtained by numerical method in ref. [1].In this paper, when the ratio of specific heat γ>>1 by using the enlargement coordinate method, the first-order analytical solutions are obtained. The perturbation parameter is ε=1/γ². The correction of these solutions is checked at the end of this paper.

A Solution of Cosine Pressures on a Hollow Cylinder and the Limit When k→0

Liu Zhu-bai, Qi Zue-yu

1993, 14(5): 419-424.

Abstract(1548) PDF(433)

Abstract:
A new stress function is found in this paper and then the problems of cosine pressures on a hollow cylinder are solved with the new stress function, which provides the basis for the solution of the problems of space symmetrical deformation of a hollow cylinder. When the pressures do not vary in the axial direction, that is, when k→0 the lame formulae can be deduced.

The Study of Surface Dust Concentration of Satellite in Fairing Separation

Huang Zhen-kan, Wang Shi-hong, Yu Li-xing, Xu Li-da

1993, 14(5): 425-433.

Abstract(1941) PDF(495)

Abstract:
The explosion process is usually used for satellite releasing during fairing separation. Explosion products are not allowed to be leaked from the detonating tube connecting two parts of the fairing during the fairing separation process. This paper predicts the contamination of the explosion products falling on the satellite surface during fairing separation on the ground and in space in case of the computer simulation by using the theory of explosion gaseous dynamics and the basic theory of aerosol mechanics.

The Singular Behaviour in the Vicinity of Intersection between the Body and Free Surface

Zhu Lin-sheng, Dai Yi-shan

1993, 14(5): 435-444.

Abstract(1586) PDF(593)

Abstract:
The singular behaviour in the vicinity of intersection between the body and free surface is presented. It is shown that in the linear regime the singularity of velocity potential for transient problem is in d²lnd. The singular behaviour for harmonic problem is the same as the result for the transient problem. In particular, the singularity for the harmonic problem with infinite frequency is in d²lnd for velocity potential (d is the distance between field point and intersection).

Explicit Criteria of Absolute Stability for the Real Second Canonical Form of Control System

Qao Guo-cheng

1993, 14(5): 445-454.

Abstract(2189) PDF(517)

Abstract:
In this paper, some explicit criteria of absolute stability for the trivial solution of the real second canonical form of non-linear control system are given, which include and improve the criteria in paper [1]. By applying these criteria to the well-known equation of the longitudinal motion of aircraft, some results are obtained, which include and improve the corresponding results in papers [1, 2, 3, 4].

Instability of Solution For the Fourth Order linear Differential Equation with Varied Coefficient

Lu De-yuan, Liao Zong-huang

1993, 14(5): 455-469.

Abstract(1897) PDF(520)

Abstract:
In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.