应用数学和力学

1995 Vol. 16, No. 1

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Solutions to Equations of Vbrations of Spherical and Cylindlical Shells

Ding Hao-jiang, Chen Wei-qiu, Liu Zhong

1995, 16(1): 1-13.

Abstract(1986) PDF(620)

Abstract:
The governing equations of the free vibrations of spherical and cylindrical shells with a regular singularity are solved by Frobenius Series Method in the form of matrix.Considering the relationship of the roots of the indicial equation,we get somevarious expressions of solutions according to different cases.This work lays a foundation of solving certain elastic problems by analytical method.

The Couple Motion Between Vessel Wall and blood in the Entrance Region of a Tapered Vessel

Cen Ren-jing, Qin Chan, Tan Zhe-dong

1995, 16(1): 15-22.

Abstract(2193) PDF(686)

Abstract:
A problem of couple motion between vessel wall and blood in the entrance region of a tapered vessel is considered in this paper.A mathematical model of co-couple action is formed for both motion of vessel wall and blood flow in the entrance regance region of elastic vessel with tapered angle.Under the situation that the relative boundary conditions are satisfied,a set of velocity distribution formula,pressure distribution formula for the blood flow in a tapered elastic vessel are derived.Some important conclusions are obtained.

Generalized Theory of Nonlinear and Unsteady Mechanics and Appliations in Partlcles Physics

Yang Wen-xiong

1995, 16(1): 23-31.

Abstract(2809) PDF(634)

Abstract:
The present paper we consider that the momentum of a high speed free particle motion appearing in nonlinear and unsteady effcts may be extended using Laurent series and their complete expressions are obtained.These phenomena also may expand to the theory of kinematics and may be determined by the first Kind of Fredholm's integral equation.In addition,according to the nonlinear and unsteady momentum obtained the relations of the nonlinear mechanics equations,work done and energy,mass and energy may be obtained.At last,this paper also calculates those results which experimented with Mu mesons,μ^± and fast neutrons motion in particles physics,these results calculated are in agreement with experiments completely.

The Inertial Fractal Set for Weakly Damped Forced Koreweg-de-Vries Equation

Dai Zheng-de, zhu zhi-we

1995, 16(1): 33-40.

Abstract(1747) PDF(552)

Abstract:
In this paper we consider weakly damped forced Kortewegde-Vries equation with non-self-adjoint operator.The existence of inertial fractal set M of this equation is proved,the estimates of the upper bounds of fractal dimension for M are also obtained.

The Bending of Thin Rectangular plates with Mixed Supported Segments of Straight Edges

Chen Li-zhi, Fu Bao-lian

1995, 16(1): 41-51.

Abstract(2218) PDF(535)

Abstract:
In this paper,the exact analytical solution of the rectangular plate having simply supported segments mixed with free segments of straight edges are first given by means of the method of reciprocal theorem.By comparison,we calculate the same problem by finite element method.The comparison shows that the analytical solution is correct.

The Existence of Limit Cycles For The System X=Q(X,y),y=p(X)

Xu Rong-liang, Zhou Guo-cai, Sun Zhao

1995, 16(1): 53-59.

Abstract(2530) PDF(590)

Abstract:
In this paper we use A.F.Filippov's method on the more generalized system x=Q(x,y),y=P(x),atheorem of the ecistence of stable limit cycles is obtained.

DynamicStress Intensity Factors around Two Cracks near an Interface of Two Dissimilar EIastic Half-PIanes under In-plane Shear Impact Load

Qian Ren-gen, Shouetsu Itou

1995, 16(1): 61-72.

Abstract(2252) PDF(479)

Abstract:
Transient stresses around two collinear cracks which lie in parallel with the interface of the two dissimilar half-planes are studied in this article.The surfaces of the cracks are sheared suddenly.Application of the Fourier and Laplace transforms technique reduces the problem to that of solving dual integrai equations.To solvethese,the differences of the crack surface displacements are expanded in a series of functions which are automatically zero outside of the cracks.The unknown coefficients accompanied in the series are determined by the Schmidt method.The stress intensity factors are defined in the Laplace transform domain and these are inverted numerically in the physical space.As an example,the dynamic stress intensity factors around two cracks in a ceramic and steel bonded composite are numerically.

Numerlcal Study of Shock Diffraction in Dusty Gases

Wu Qing-son, Zhu Hong, Xu Yan-hou, Wang Bo-yi

1995, 16(1): 73-79.

Abstract(2131) PDF(502)

Abstract:
In the present paper.a two-fluid model with interphase coupling effects is appliedto dilute gas-particle systems.In order to study,the characteristics of shock diffraction round a sharp 90 degree corner in the dusty gas,we adopt the operator-spliting technique and high-resolution numerical method,reveal the changes of diffraction pattern due to particle presence,and discuss the effects of particle properties onpost-shock flow field.

The Remainder-Effect Analysis of Finite Differencee Schemes and the Applications

Liu Ru-xun, Zhou Zhao-hui

1995, 16(1): 81-90.

Abstract(1988) PDF(572)

Abstract:
In the present paper two contents are enclosed.First,the Fourier analysis approach of the dispersion relation and group velocity effect of finite difference schemes is discussed.the defects of the approach is pointed out and the correction is made;Second,a new systematic analysis method-remaider-effect analysis(abbr.REAM) is proposed by means of the modified partial differential equations(abbr.MPDE) of finite difference schemes.The analysis is based on the synthetical study of the rational dispersion and dissipation relations of finite difference schemes.And the method clearly possesses constructivity.

An lnterpolation Fomula of the Derivatives of Higher Order

Gui Zu-hua

1995, 16(1): 91-94.

Abstract(2049) PDF(734)

Abstract:
In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.