应用数学和力学

1990 Vol. 11, No. 2

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A Non-Dualistic Unified Field Theory of Gravitation,Electromagnetism and Spin

Yu Xin

1990, 11(2): 95-109.

Abstract(1880) PDF(448)

Abstract:
The wisdom of classicalunified field theories in the conceptual framework of Weyl,Eddington,Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell(E-MJ theory needs to be geometrized.The crux of the matter is,howeve...

Effects of Bottom Topography on the Standing Waves in Circular Basins

Ma Yun-li, Li Jia-chun

1990, 11(2): 111-118.

Abstract(1481) PDF(539)

Abstract:
Standing waves in the cylinder hasins with inhomogeneous bottom are considered in this paper.We assume that the inviscid,incompressible fluid is in irrotational undulatory motion.For convenience sake,cylindrical coordinates are chosen.The velocitv potentials,the wave profiles and the modified freque...

On the Existence of Limit Cycles of Liénard Equation

Huang An-ji, Cao Deng-qing

1990, 11(2): 119-130.

Abstract(1815) PDF(452)

Abstract:
In this paper,we have proved several theorems which guarantee that the Liénard equation has at least one or n limit cycles without using the traditional assumption G(±∞)=+∞ Thus some results in [3-5] are extended.The limit cycles can be located by our theorems.Theorems 3 and 4 give sufficient condit...

The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅱ)

Zhang Jing-zhong, Yang Lu, Zhang Lei

1990, 11(2): 131-140.

Abstract(1809) PDF(436)

Abstract:
In recent years,there is a wide interest in Sarkovskii's theorem and related study.According to Sarkov.lkii's theorem,if the continuous self-map f of the closed interval has a 3-periodic orbit,then f must has an n-periodic orbit for any positive integer n.But f can not have all n-periodic orbits for...

Optimizing Formulation of Hybrid Model for Thin and Moderately Thick Plates

Di Sheng-lin, Wu Chang-chun, Song Qi-gen

1990, 11(2): 141-148.

Abstract(1909) PDF(476)

Abstract:
A 20-DOF hybrid stress element based upon Mindlin plate theory is developed using the optimization design method for thin and moderately thick plates.Numerical tests consist of the convergency and performance to the plates with arbitrary thickness and shape and of the ultimate thin plate problems.

The Sudden Starting of a Floating Body in Deep Water

Tao Ming-de

1990, 11(2): 149-154.

Abstract(1766) PDF(403)

Abstract:
This paper applies Lagrangian method to discuss the sudden starting of a floating hotly in deep water and the analytical'solutions are obtained.It is known from the numerical results that the disturbing domain extends and the dynamic pressure also increases when the breadth of the floating body keep...

Exact Solutions for Stationary Responses of Several Classes of Nonlinear Systems to Parametric and/or External White Noise Excitations

Zhu Wei-qiu

1990, 11(2): 155-164.

Abstract(1940) PDF(632)

Abstract:
The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-Planck-Kolmogorov et/ualion approach.The conditions for the existence and uniqueness...

General Dynamic Equation and Dynamical Characteristics of Viscoelastic Timoshenko Beams

Xiao Can-zhang, Ji Yi-zhou, Chang Bao-ping

1990, 11(2): 165-172.

Abstract(1948) PDF(682)

Abstract:
In this paper,a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method.To measure the complex moduli and three parameters of standard linear solid,the forced vibration technique of beam is successf...

The Application of Boundary Element Method in Stress Analysis of Autofretted Tube with Notch

Song Shun-cheng, Zhang Yu-cheng, Feng De-zhen

1990, 11(2): 173-178.

Abstract(1814) PDF(418)

Abstract:
In this paper,the boundary element method is applied to investigate the internal state of stress of autofretted tube with notch and the calculated results are important in the practical design.

Calculation for Cylindrical Shell under Local Vertical Loadings

Sun Ren-bo, Wang Dai-yu, Zou Ding-qi

1990, 11(2): 179-188.

Abstract(1892) PDF(627)

Abstract:
In this paper,we use the method of mixed-type series to derive the analytical solutions of cylindrical shell,which is simply supported along the transverse edges and subjected to the local vertical loads,and give the analytical expressions of the solutions for this kind of shell under five types of ...