应用数学和力学

1985 Vol. 6, No. 11

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The Global Analysis of Higher Order Non-linear Dynamical Systems and the Application of Cell-to-Cell Mapping Method

C. S. Hsu, Xu Jian-xue

1985, 6(11): 953-962.

Abstract(2268) PDF(849)

Abstract:
In this paper, the general characteristics and the topological consideration of the global behaviors of higher order nonlinear dynamical systems and the characteristics of the application of cell-to-cell mapping method in this analysis are expounded. Specifically, the global analysis of a system of ...

Tsai Shu-tang, Liu Yi-xin

1985, 6(11): 963-968.

Abstract(1981) PDF(585)

Abstract:
In the preceding article^[1], the relation between thermodynamics condition and inceptive cavitation stage has been discussed. In this paper, we try to introduce the volume function of inceptive cavitation bubbles, z₀(r), instead of the energy equation used in the reference ^[1],for discussing cavitat...

Generalized Airy Functions with Complex Variables

Li Jia-chun, Zhao Da-gang

1985, 6(11): 969-975.

Abstract(2172) PDF(633)

Abstract:
In the present paper, we have made a detailed study of the generalized Airy functions, which have found wide applications in the field of wave propagation and hydrodynamic stability. A series of tables and graphs are provided for the above functions with complex variables. The results are proved sat...

The Mixed Mode Brittle Fracture Criteria in Sliding Mode Fracture

Lin Bai-song

1985, 6(11): 977-983.

Abstract(2031) PDF(624)

Abstract:
It is well-known that the present mixed mode brittle fracture criteria are all the opening mode fracture criterion. We consider that mixed mode brittle fracture of sliding mode fracture exists too. Hence we propose three criteria of mixed mode brittle fracture of sliding mode fracture; the radial sh...

Application of the Reciprocal Theorem for Calculating the Natural Frequencies of Rectangular Elastic Thin Plates

Fu Bao-lian

1985, 6(11): 985-997.

Abstract(1911) PDF(844)

Abstract:
This paper further extends the applications of the reciprocal theorem to calculating the natural frequencies of rectangular elastic thin plates on the basis of [1]. Applying the presented method, there is no need to solve governing differential equations, it is only necessary to solve a simple integ...

Nonlinear Kelvin Helmholtz Instability

Chen Le-shan

1985, 6(11): 999-1012.

Abstract(2381) PDF(621)

Abstract:
A non-linear analysis is presented with derivative expansion method for the inter facial stability of a liquid film adjacent to a subsonic gas flow under the influence of body force and surface tension. The non-linear Rayleigh-Taylor instability is included as a special case. The gas and liquid are ...

On the Finite Displacement Problem of a Hollow Sphere under Internal and External Pressures

Huang Ze-yan

1985, 6(11): 1013-1018.

Abstract(2187) PDF(611)

Abstract:
Taking advantage of successive approximations, the present boundary-value problem is solved. We find the first-order and second-order solutions, and therefore we obtain the formulae in the second approximation for the displacement, strain, and stress fields.

Stress Intensity Factor Considering the Material Plasticity Limited in Scope

1985, 6(11): 1019-1026.

Abstract(1841) PDF(644)

Abstract:
For the practical metallic material, preceding the fracture, there always exist the domains of plasticity. For the plasticity limited in scope, the linear elastic mechanics is still applicable, but it is neccesary to correct the influence of the domain of plasticity. The traditional method of correc...

Proper Solutions and Limit Boundary Value Problems of Nonlinear Second-Order Systems of Differential Equations

Liang Zhong-chao, Chen Shao-zhu

1985, 6(11): 1027-1034.

Abstract(2383) PDF(626)

Abstract:
For the system of differential equations , where a(t)>0, r(t)>0 for t≥t₀, f(x) >0 and is decreasing for x>0 g(y)>0, we give necessary and sufficient condition of the existence of a proper solution, a bounded proper solution or solutions of two kinds of boundary value problems on an in...

Effects of Hunting on the Stability of Ecosystems

Wang Fu-jun

1985, 6(11): 1035-1041.

Abstract(2207) PDF(612)

Abstract:
In this present paper, we examine the effects of hunting on the stability of prey-predator systems and grazing systems. The theory of stability and singular perturbation method are applied for analysing.