应用数学和力学

1994 Vol. 15, No. 6

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Geometrically Nonlinear Analysis of Mindlin Plate Using the Incompatible Bending Elements with Internal Shear Strain

Jiao Zhao-ping, Wu Chang-chun, T. H. H. Pian

1994, 15(6): 479-488.

Abstract(2093) PDF(585)

Abstract:
An approach of the incompatible elements with additional internal shear strain is suggested and applied to geometrically nonlinear analysis of Mindlin plate bending problem, It provides a quite covenient way to avoid the shear locking troubles. An energy consistency condition for this kind of C⁰ elements is offered.The nonlinear element formulations and some numerical results are presented.

The Application of the Variational Principle in the Constrained Control System

Deng Zi-chen, Zhong Wan-xie

1994, 15(6): 489-494.

Abstract(1641) PDF(486)

Abstract:
The regular equations on the constraint variables are established for LQ and nonlinear control problems in this paper,then the extreme-value principles of the constraint variables are discussed for the equality and unequalitp constraint cases respectively.At lasi,the given ecample verifies the conclusion of this paper, The work in this paper will lay the foundation for the furthe study about the constrained LQ and nonlinear control spstems.

Non-Linear Vibration of Rectangular Retlculated Shallow Shell Structures

Nie Guo-hua

1994, 15(6): 495-504.

Abstract(2159) PDF(521)

Abstract:
This paper deals with non-linear vibration of rectangular reticulated shallow shells by applying non-linear elastic theory of such structures established by the author. Using the assumed(generalized) Fourier series solutions for transverse deflection(lattice joint transverse displacement) and force function，weighted means of the trial functions lead to the relations among the coefficients related to the solutions and vibration equation which determines the unknown time function, and then the amplitude-frequency relations for free vibration and forced vibration due to harmonic force are derived with the aid of the regular perturbation method and Galerkin procedure, respectively.Numerical ezamples are given as well.

The Motion of a Sphere with Weak Nutation on a Rough Horizontal Plane

Yang Ji-ying

1994, 15(6): 505-512.

Abstract(1776) PDF(519)

Abstract:
For the motion of a sphere on a rough horizontal plane, in the previous paper [1],the author aimed at providing approximate analytical solutioas while the nutation is neglected. In this paper,the control equations for the sphere with nutation have been deduced on the basis of paper [1].Through the medium of solving these equations, the conclusion for the velocity of contact point in paper [1] is still proved true for the case with nutation.What is more,some interesting results are gained,for example.,the velocity of centre and contact point is relative to the angular velocity of spin and nutation the direction of velocity of centre and contact point is constant.Under the condition which is supposed to be weak nutation,the approximate analytical solutions are obtained,so that the results of paper [1] is proved to be true.

On the Stability of the Solution to a Gonorrhea Discrete Mathematical Model

Jin Jun

1994, 15(6): 513-518.

Abstract(1979) PDF(433)

Abstract:
In this paper, the author studies the stability of the solutioa to a three dimensional gonorrhea discrete mathematical model by Liapunov method.The parameter estimator of the stability domain is obtained and the rationality of the model is explained in a theoretic way.

Matrix Perturbation Methol for the Vibration Problem of Structures with Interval Parameters

Qiu Zhi-ping, Chen Su-huan, Liu Zhong-sheng

1994, 15(6): 519-527.

Abstract(2072) PDF(540)

Abstract:
When the parameters of the structures are uncertain, the structural natural frequencies become uncertain.In this paper, we deal with the vibration problem of the structure with interval parameters,the eigenvalue problem of the structures with interval parameters is transferred into two different eigenvalue problems to be solved. The perturbation method is applied to the vibration problem of the structures with interval parameters, the numerical results show that the proposed method is sufficiently accurate and needs little computational efforts.

Mixed Compatible Element and Mixed Hybrid Incompatible Element Variational Methods in Dynamics of Viscous Barotropic Fluids

Shen Xiao-ming

1994, 15(6): 529-537.

Abstract(2328) PDF(465)

Abstract:
This paper presents and proves the mixed compatible finite element variational principles in dynamics of viscous barotropic fluids.When the principles are proved, it is found that the com patibility conditions of stress can be naturaly satisfied, The generalized variational principles with mixed hybrid incompatble finite elements are also presented and proved,and they can reduce the computation of incompatible elemenis in dynamics of viscous barotropic lows.

Attractors of Oisslpative Soliton Equation

Tian Li-xin, Xu Zhen-yuan, Liu Zeng-rong

1994, 15(6): 539-547.

Abstract(1826) PDF(627)

Abstract:
In this paper,we study longtime dynamic behavior of dissipative soliton equations existence of attractor, geometrical structure of attractor, dynamic behavior under the parametric perturbation of dissipative soliton equation, estim ate of fractal dimension of attractor.

Dissipative Effects of an Isolated Bubble in Water on the Sound Wave

Huang Jing-quan, Li Fu-xin

1994, 15(6): 549-554.

Abstract(1961) PDF(613)

Abstract:
The dissipative mechanisms of an isolated bubble in water for souad wave are analysed on the basis of the linearized theory of oscillations of a gas bubble.It is shown that the dissipative effects are obvious and contain the scattering and absorption of sound by a bubble;the heat conduction is decisive in the dissipative effects of bubble:a nd the dissipative effects are mazimum it resonance.

The Influence of Topography on the Nonlinear Interaction of Rossby Waves in the Barotropic Atmosphere

Xiong Jian-gang, Yi Fan, Li Jun

1994, 15(6): 555-563.

Abstract(1998) PDF(504)

Abstract:
In the frame of weak nonlinear theory,a set of equations depicting the nonlinear iateractioas of barotropic Rossby waves are derived,the topography and Ekman friction are involved in the equations. Starting from the equations, we investigate the interaction of three Rossby wave packets with narrow-spread in wave vectors, When an intense primary pump Rossby wave with amplitude larger than a threshold propagates through the atmosphere, the amplitude of one Rossby wave packet with scale greater than the primary one and one Rossby wave packet with scale smaller than the primary one grow exponentially through three wave interactions, the intrinsic frequencies of the secondary waves can be varied. The threshold and the variation of the intrinsic frequencies of the secondary waves are related to the Ekman friction frequency dismatch,topography and spatial evolution of the secondary Rossby wave packets.

The Derivation of Exact Static Conditions at the Corner Points for the Bending of Thick Rectangular Plates

Fu Bao-lian

1994, 15(6): 565-570.

Abstract(1966) PDF(437)

Abstract:
In this paper,exact static conditions at the corner points for the bending of thick rectangular plates are strictly derived from the theorem of minimum potential energy.