应用数学和力学

1996 Vol. 17, No. 7

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Atomization of a Liquid Drop by Pulsation

S. P. Lin, Z. W. Zhou

1996, 17(7): 569-576.

Abstract(2363) PDF(502)

Abstract:
By using stability analysis, it is shown that a spherical drop can be resonated parametrically to initiate the formation of droplets of diameters much smaller than that of the original drop. Both the surface tension and the density of the surrounding gas tend to retard this atomization process. The interfacial instability associated with the D'Alembert apparent body force in two superposed flat fluid layers is shown to be closely related to the interfacial instability caused by parametric resonance.

The Analytical Study on the Laser Induced Reverse-Pluggaing Effect by Using the Classical Elastic PlateTheory(Ⅱ)──Reversa-Bulge. Motion

Zhou Yichun, Duan Zhuping, Xie Bomin

1996, 17(7): 577-588.

Abstract(2037) PDF(421)

Abstract:
Tile reverse-bulge motion(RBW) in the metallic foils. which is induced by spatially cylindrical long pulse laser. is examined in order to analyse the newly-discovered reverse-plugging effect(RPE). An uncoupled, thin plate theory is Used to determine the induced. flexural vibrations. The solution is obtained as the superposition of two displacement. fields, representing the quasi-static and the dynamic behaviors.Meanwhile. the equivalent thermal loading and the dimensionless analysis of thin plate motion are presented. Numerical results presented may partially explain the RBM of thin plate at the early stage of laser irradiation.

Nonlinear Three-Dimensional Analysis of Composite Laminated Plates

Jiang Xiaoyu, Zhang Xiangzhou, Chen Baipin

1996, 17(7): 589-600.

Abstract(1996) PDF(483)

Abstract:
In this paper. an analytic method is. presented. for the research of nonlinear Three-dimensional problems of composite laminated plates. The perturbation method and the variational principle are used to satisfy the basic differential equations and the boundary conditions of the three-dimensional theory of elasticity. The nonlinear three-dimensional problems are studied. for composite anisotropic circular laminas and laminates subjected to transverse loading. The perturbation series solutions of high accuracy are obtained. A large number of results show that transverse normal stress and transverse shear stresses are very important in the nonlinear three-dimensional analysis of laminated plates.

Double High Order S-Breaking Bifurcation Points and Their Numerical Determination

Yang Zhonghua, Ye Ruisong

1996, 17(7): 601-612.

Abstract(1546) PDF(427)

Abstract:
We consider double high order S-breaking bifurcation points of two-Parameter dependent nonlinear problems with Z₂×Z₂-symmetry. Because of the underlying symmetry we could propose some regular extended systems to determine double high order S-breaking bifurcation points. and we could also show that there exist two quadratic pitchfork bifurcation point paths passing through the point being considered.

A Three-Fluid Model of the Sand-Driven Flow

Liu Dayou, Dong Fei

1996, 17(7): 613-624.

Abstract(2027) PDF(501)

Abstract:
The sand-driven flow is studied from the continuum viewpoint in this paper. The crux of this work is how to model the stresses of the particle phase properly. By analysing the two-fluid model which usually, works in solving gas-particle two-phase. flow,. we find that this model has many. deficiencies for studying the sand-driven flow,even for the simplest case-the steady, two-dimensional fully-developed flow.Considering this, we have proposed the three-fluid model in which the upward particles and the downward-particles ore regarded as two kinds of fluids respectively.It is shown that the three-fluid model is better than the two-fluid model in reflecting the internal structure of the flow, region and the influence of the boundary situations on the flow. and it is advantageous to find an approximate solution in that the main components of the particle-phase stresses can be explicitly expressed by those variables in the three-fluid model.In the end, the governing equations as well as the boundary. conditions for the three-fluid model are provided with a discussion.

Newton’s Theorem with Respect to a Lot of Centers and Their Applications

Gut Zuhua

1996, 17(7): 623-627.

Abstract(1817) PDF(527)

Abstract:
In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.

The General Method for Solving the Dynamic Problems

Sun Youlie

1996, 17(7): 629-638.

Abstract(2023) PDF(424)

Abstract:
In this paper the author has used the normalized Routh equations^[1] to. solve the dynamic problems and establish the general method for. finding out the constraint forces and the variations of the state of motion for the complicated systems.

Analysis of Dynamic Responce of an impacted Elastic Plate

Yin Bangxin

1996, 17(7): 639-644.

Abstract(2189) PDF(635)

Abstract:
In [1], the dynamic response of an impacted elastic plate is analysed. Using the method in [1] is on condition that impacting body is rigid and the relation between impact reacting. force and partial deformation is known In this paper. Simulate formula of impact reacting force. function is presented. Without assumption of impacting body, dynamic response in impact procedure is considered avoiding the problem of partial deformation. Because of analysis by law of momentum conservation. impulse theorem, dynamic differential equation and numerical method the method in this paper is more suitable for application. Examples of the application are given. In precision, solution in this paper is identical with known correct solution.

Relativistic Variation Principles and Equation of Motionfor Variable Mass Controllable Mechanical Systems

Luo Shaokai

1996, 17(7): 645-653.

Abstract(2393) PDF(530)

Abstract:
With classical variable mass and relativistic variable mass cases being considered.the relativistic D'Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation. for variable mass controllable mechanical system in quasi-coordinates and generalized-coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed.

Solving Vibration Problem of Thin Plates Using Integral Equation Method

Xu Mingtian, Cheng Delin

1996, 17(7): 655-660.

Abstract(2192) PDF(807)

Abstract:
This paper deals with reducing differential equations of vibration problem of plates with concentrated masses, elastic supports and elastically mounted masses into eigenvalue problem of integral equations. By applying the general function theory and the integral equation theory. the frequency equation is derived in terms of standard eigenvalue problem of a matrix with infinite order. So that, the natural frequencies and mode shapes can be determined. Convergence of this method has also been, discussed at the end of this paper.

M. E. Shvez lterative Method and its Application in Mechanics

Yuan Yiwu, Liu Youwen

1996, 17(7): 661-666.

Abstract(2091) PDF(500)

Abstract:
When there is small quantity term contained in differential equation, we may solve if by using the M.E.Shvez iterative method. If foe small quantity term has singularity, of in foe certain region where foe small quantity term is not small, using this method to solve such differential equation, we may meet difficulties. In this paper,the author improves the M.E.Shvez method. Several examples are given to demonstrate the algorithm.