应用数学和力学

1992 Vol. 13, No. 1

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Elastic Dynamics Variational Principle for Nonlinear Elastic Body

Zhang Ru-qing

1992, 13(1): 1-9.

Abstract(2276) PDF(440)

Abstract:
Based on paper [1],the variational principle and generalized variational principle of elastic dynamics for elastic body with nonlinear stress-strain relations are introduced in this paper.The generalized instantaneous variational principle is also raised for the mixed harmonious displacement element and the mixed harmonious stress element.

Stochasticity near Resonances in a kind of Near-lntegrable Hamiltonian Systems Based on Smale Horseshoes

Dong Guaug-mao, Liu Zeng-rong, Xu Zheng-fan

1992, 13(1): 11-16.

Abstract(2201) PDF(459)

Abstract:
In this paper,a method is developed to detect the appearance of stochasticity in a kind of near-integrable Hamiltonian system with two time-scales.One is fast and the other slow.The stochasticity is showed to be chaos in the sense of Smale horseshoes actually.A stochastic web is discovered in our example,by use of the results obtained in this paper.

Vibration Characteristics of Offshore Cylindrical Tanks

Zhu yong-yi, Weng Zhi-yuan, Wu Jia-long

1992, 13(1): 17-26.

Abstract(2220) PDF(424)

Abstract:
The vibration characteristics of offshore cylindrical tanks are studied in this paper.This is a typical topic of liquid-shell interaction system.In this paper,a general analytical method is presented by which the axial modal functions of liquid and shell are represented as the same complete orthogonal series for uncoupling the mode of liquid and shell.Simultaneously,the mode functions are expanded into a uniform convergence series and a linear polynomial,so that the problem.of convergence and differentiation of mode series is solved.Therefore,the rather exact natural frequency and its corresponding mode of off shore cylindrical tank with different liquid depths,with arbitrary boundary conditions and with intermediate constraints can be obtained.

On Internal Resonance of Nonlinear Vibrating Systems with Many Degrees of Freedom

S. L. Lau, Xu Zhao

1992, 13(1): 27-34.

Abstract(2007) PDF(894)

Abstract:
The problem of periodic solutions of nonlinear autonomous systems with many degrees of freedom is considered.This is made possible by the development of a modified version of the KBM method[1].The method can be used to generate limit cycle phase portrait,amplitude,period and to indicate stability of the limit cycle.

Rossby Waves with the Change of β

Liu Shi-shi, Tan Ben-kui

1992, 13(1): 35-44.

Abstract(2195) PDF(533)

Abstract:
In this paper,the change of the Rossby parameter β with latitude is considered and the parameter γ≡dβ/dy=2sinφ/a² is introduced and the β-plane approximation is extended into f=f₀+β₀y-γ₀y²/2 which includes the parameter γ.Such approximation closes further to practice especially in the high latitude regions.We give emphasis to the research of the effect of the parameter γ on the Rossby waves.It is seen that the effect of the parameter γ is remarkable in the high latitude regions.It can produce the Rossby waves caused by the pure parameter γ.And the phase speed formula of Rossby waves with the change of ft is generally given,which is degenerated into the well-known Rossby formula when γ₀=0.The researches also point out that when the change of β is regarded,even if the basic current u is a linear function of y the unstable modes can also take place.However,the parameter γ usually plays a stable part in the Rossby waves and it does affect the longitudinal scale and the structure of constant phase lines(trough-ridge lines) of Rossby waves and slow down the growing or decaying of Rossby waves.

Non-lntegrability and Chaos of a Conservative Compound Pendulum

Ling Fu-hua, Xu Ru-jin

1992, 13(1): 45-52.

Abstract(2743) PDF(634)

Abstract:
By using a series of canonical transformations(Birkhoff's series),an approximate integral of a conservative compound pendulum is evaluated.Level lines of this approximate integral are compared with the numerical simulation results.It is seen clearly that with a raised energy level,the nearly integrable system becomes non-integrable,i.e.the regular motion pattern changes to the chaotic one.Experiments with such a pendulum device display the behavior mentioned above.

Bending of Cantilever Rectaugular Plates with the Effect of Transverse Shear Deformation

Yang Xiao, Ning Jian-guo, Cheng Chang-jun

1992, 13(1): 53-66.

Abstract(2178) PDF(644)

Abstract:
On the basis of Reissner's theory,the exact solutions of the bending of cantilever rectangular plates are obtained by means of the concept of generalized simply-supported boundary.From the results obtained,it can be found that the method is valid.

Singularly Perturbed Semilinear Elliptic Equation with Boundary-Interior Layer Interaction

Zhou Zhe-yan

1992, 13(1): 67-79.

Abstract(2004) PDF(510)

Abstract:
In this paper,we consider the phenomenon of the boundary and interior layer interactions for a class of semilinear elliptic equation.Under some appropriate conditions,we get the existence of the exact solution for the problem and its high order uniformly valid expansion.

Exponential Dichotomies of Nonlinear Discrete Systems and Its Application to Numerical Analysis and Computation

Zhang Wei-jiang

1992, 13(1): 81-88.

Abstract(1964) PDF(434)

Abstract:
In this pepar we consider the upwind difference scheme of a kind of boundary value problems for nonlinear,second order,ordinary differential equations.Singular perturbation method is applied to construct the asymptotic approximation of the solution to the upwind difference equation.Using the theory of exponential dichotomies we show that the solution of an order-reduced equation is a good approximation of the solution to the upwind difference equation except near boundaries.We construct correctors which yield asymptotic approximations by adding them to the solution of the order-reduced equation.Finally,some numerical examples are illustrated.

Surface Instability of Elastic Half Spaces with Hydrostatic Loading on Their Surfaces

Cao Guang-zhong, Xu Zhi-hong

1992, 13(1): 89-102.

Abstract(2162) PDF(481)

Abstract:
In this paper,the plane-strain buckling of compressible and incompressible elastic half-spaces,whose surfaces are loaded by constant hydrostatic pressures,is studied by using a small-deformation-superposed-on-large-deformation analysis,and the buckling condition for each case is obtained.For Blatz-Ko and harmonic compressible materials as well as Mooney incompressible material,the influence of the surface hydrostatic pressure on the critical buckling condition is discussed in detail.