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1994年 第15卷 第9期    刊出日期：1994-09-18

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论文

A COMPARISON OF FOUR RECENT NUMERICAL SCHEMESGIViNG HIGH RESOLUTION OF SHOCK WAVEAND CONCENTRATED VORTEX

黄敦;杨淳

1994, 15(9):  797-804. 

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In recent ten years high resolution difference schenies for the computation of thefull unsteady Eulerian system of equations for invisid compressible gas finds celebratedprogress. This paper tests furtherly, by a complex two-dimensional unsteady problem,four recent schemes. to them attentions are paid. The test problem is the initial stageof a two-dimensional diffraction and reflection of a plane shock wave, impinging on arectangular obstacle. At whose top side there are two sharp corners, near which flow.parameters finds severe variation. There is occurrence of expansion fan with a centerand also concentrated vortices. To simulate them well, the schemes should have goodadaptivity. The special shock Mach number M₁=2.068 is so chosen, that at this M₁,the partical velocity behind impinging shock in fixed coordinate system is just equal tothe speed of sound there, this condition also occurs along a curve in the region ofexpansion fan with a center at the corner. This can clarify the computational featureof different schemes in case,when one of the eigenvalues is just zero. Zero eigenvaluemay spoil some schemes locally. Graphical visualization of the computational resultsmay, show features of the tested schemes about the shock wave resolution, schemeviscosity, expansion wave and the ability. to simulate the process of the generation ofunsteadv concentrated vortex.

GENERALIZED VARIATIONAL PRINCIPLES OF SYMMETRICALELASTICITY PROBLEM OF LARGE DEFORMATIONS

赵玉祥;顾祥珍;李欢秋

1994, 15(9):  805-813. 

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This paper is based on the geometrical nonlinear theories of deformationpresented by Chen Zhi-da^[1], Lagrange's multiplier mothod is used to study thesymmetry elasticity problems of large deformation. The general rariational priieiplesof potential energy and coinplemenlary energy,and the general variation principle ofdynamic problem have been proved. In the meantme it is also proved that the generalvatiaton principles of potential energy and complementary energy are equivalent.

ON THE INVERSE PROBLEM IN CALCULUS OF VARIATIONS

梁立孚;石志飞

1994, 15(9):  815-829. 

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The inverse problem in calculus of variation is studied. By introducing a newconcept called Varialional Integral, a new method to systematically study the inverseproblem in calculus of rariations is given. Using this new method to the elastodynamicsand hydrodynamics of viscous fhuids some kinds of variaiional principles andgeneralized variational prineiples are obtained respectively.

FREE BENDING VIBRATION OF ANNULAR CYLINDRICALTANK PARTIALLY FILLED WITH LIQUID IN THECONSIDERATION OF SURFACE WAVE

周叮

1994, 15(9):  831-839. 

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This paper studies the problem of free bending vibration of annular cylindricaltank partially filled with liquid in the consideration of surface wave.The exactformulae of the mode shape functions and frequencies are deduced.Results can beobtained by means of computer.The analysis shows that the effect of liquid on vibration of annular cylindrical tank is equivalent to different generalized distributivemasses attached to inner and outer cylinders respectively.

FINITE ELEMENT ANALYSIS FOR THE UNSTEADY NEARSHORECIRCULATION DUE TO WAVE-CURRENT INTERACTION (II)──TWO-STEP EXPLICIT FINITE ELEMENT METHOD

吴伟雄

1994, 15(9):  841-848. 

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In this paper, the two-step explicit finite element analysis for the numerical modelof the unsteady nearshore circulation proposed in Ref [1]and its realization of Fortranprogram are presented.A circulation has been clearly shown in the calculated wave-current velocity field,and it is in good agreement with observations

AN ANALYTICAL SOLUTION OF SECOND-ORDER WAVE FORCEON A VERTICAL CIRCULAR CYLINDER

邹志利;戴遗山

1994, 15(9):  849-863. 

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So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.

STABILITY OF NAVIER-STOKES EQUATION(Ⅰ)

施惟慧

1994, 15(9):  865-866. 

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In this paper we give an example of non-uniqueness of local solution for somekinds of boundary value problem of Navier-Stokes equation.

OSCILLATION THEOREMS OF HIGHER ORDER NONLINEARDELAY DIFFERENTIAL EQUATIONS

靳明忠

1994, 15(9):  867-875. 

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This paper has given necessary and sufficient conditions for oscillation of a classof higher order nonlinear delay differential equations, and given some sufficientconditions or necessary conditions for oscillation of a forced delay differentialequation.

NOETHER'S CONSERVATION LAWS OF HOLONOMIC NONCONSERVATIVEDYNAMICAL SYSTEMS IN GENERALIZED MECHANICS

乔永芬;岳庆文;董永安

1994, 15(9):  877-883. 

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In the present paper, three kinds of forms for Noether's conservation laws of hol-onomic nonconservative dynamical systems in generalized mechanics are given.

STABILITY OF THE KORTEWEG-DE VRIES SOLITARY WAVE SOLUTION

吕咸青

1994, 15(9):  885-886. 

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This paper considers the stabilily of the Korteweg-de Vries solitary wave solutionwith respect to infinitesmal dislurbance. It is found that the Korteweg-de Vries solitarywave solulion. is unstable in the Liapunov sense.

ANALYSIS OF THE ECCENTRIC CYLINDRICAL THIN SHELL

常明;常琍琍

1994, 15(9):  887-895. 

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The present paper gives the approximate equations of the eccentric cylindricalthin shell under small deflections. Br means of the analytical method, we solved theequations. Thus the relations between the stress, the displacement and the eccentricityof the eccentric cylindrical thin shell are obtained.