Table of Content

18 June 1994, Volume 15 Issue 6

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Articles

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):  507-516. 

Abstract ( 581 )   PDF (507KB) ( 978 )  

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An approach of the incompatible elements with additional internal shear strain is,in the presem paper,suggested and applied to geometrically nonlinear analysis of Mi-ndlin plate bending problem. It provides a quite covenient way to avoid the whear loc-king troubles. An energy consistency condition for this kind of C° 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):  517-528. 

Abstract ( 530 )   PDF (344KB) ( 485 )  

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The regular equations on the constraint variables are established for LQ and non-linear control problems in this paper,then the extreme-value principles of con-straint variables are discussed for the equality and unequality constraint cases respec-tively. At last, the given example verifies the conclusion of this paper. The work in this paper will lay the foundation for the further study about the constrained LQ and non-linear control systems.

NON-LINEAR VIBRATION OF RECTANGULAR RETICULATED SHALLOW SHELL STRUCTURES

Nie Guo-hua

1994, 15(6):  525-535. 

Abstract ( 571 )   PDF (535KB) ( 466 )  

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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. Us-ing the assumed (generalized) Fourier series solutions for transverse deflection (latticejoint transverse displacement)and force function,weighted means of the trial functions lead to the relations among the coefficients related to the solutions and vibration equ-ation which determines the unknown time function,and then the amplitude -frequeney relations for free vibration and forced vibration due to harmonic force are derived withthe aid of the regular perturbation method and Galerkin procedure,respectively. Nu-merical examples are given as well.

THE MOTION OF A SPHERE WITH WEAK NUTATION ON A ROUGH HORIZONTAL PLANE

Yang Ji-ying

1994, 15(6):  537-547. 

Abstract ( 545 )   PDF (433KB) ( 532 )  

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For the motion of a sphere on a rough horizontal plane, in the previous paper [1] the author aimed at providing approximate analytical solutions while the nutation is neglected,In this paper, the control equations for the sphere with nutation have beendeduced 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 ve-locity of centre and contact point is relative to the angular velocity of spin and nuta-tion the direction of velocity of centre and contact point is constant. Under the condi-tion 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):  545-550. 

Abstract ( 631 )   PDF (298KB) ( 636 )  

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In this paper, the author studies the stability of the solution to a three-dimension-al gonorrhea discrete mathematical model by Liapunoy method. The parameter es-timator of the slability domain is obtained and the rationality of the model is ex-plained in a theoretic way.

MATRIX PERTURBATION METHOD FOR THE VIBRATION PROBLEM OF STRUCTURES WITH INTERVAL PARAMETERS

Qiu Zhi-ping;Chen Su-huan;Liu zhong-sheng

1994, 15(6):  551-560. 

Abstract ( 589 )   PDF (534KB) ( 516 )  

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When the parameters of the structures are uncertain, the structural natural frequ-encies become uncertain. In this paper, we deal with the vibration problem of the struc-ture with interval parameters, the eigenvalue problem of the structures with intervalparameters is transferrd into two different eigenvalue problems to be solved. The per-turbation method is applied to the vibration problem of the structures with interval pa-rameters, the numerical results show that lhe proposed method is sufficiently accurateand 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):  561-569. 

Abstract ( 625 )   PDF (495KB) ( 527 )  

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This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.

ATTACTORS OF DISSIPATIVE SOLITON EQUATION

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

1994, 15(6):  571-578. 

Abstract ( 564 )   PDF (438KB) ( 739 )  

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In the paper, we study longtime dynamic behavior of dissipative soliton equation existence of attractor, geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equation. estimate of fractal dimension of attractor.

DISSIPATIVE EFFECTS OF AN ISOLATED BUBBLE IN WATER ON THE SOUND WAVE

Hunag Jing-quan;Li Fu-xin

1994, 15(6):  579-584. 

Abstract ( 597 )   PDF (336KB) ( 575 )  

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The dissipative mechanisms of an isolated bubble in water for sound wave are analysed on the basis of the linearized theory of oseillations of a gas bubble. It isshown that the dissipative effects are obvious and contain the scattering and absorptionof sound by a bubble the heat conduction is decisive in the dissipative effects of bu-bble; and the dissipative effects are maximum at 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):  585-594. 

Abstract ( 618 )   PDF (541KB) ( 514 )  

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In the frame of weak nonlinear theory, a set of equations depicting the nonlinear interactions of barotropic Rossby waves are derived, the topography and Ekman fric-tion are involved in the equations. Starting from the equations,we investigate the in-teraction 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 greaterthan the primary one and one Rossby wave packet with scale smaller than the primaryone grow exponentially through three wave interactions,the intrinsic frequencies of the secondary waves can be varied, The threshold and the variation of the intrinsic frequ-encies of the secondary waves are related to the Ekman friction frequency dismatchtopography 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):  595-600. 

Abstract ( 654 )   PDF (254KB) ( 495 )  

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In this paper, exact static conditions at the corner points for the bending of thickrectangular ptates are strictly. derived from the theorem of minimum potentialenerg[1].