应用数学和力学

1989 Vol. 10, No. 10

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Exact Analytic Method for Solving Variable Coefficient Differential Equation

Ji Zhen-yi, Ye Kai-yuan

1989, 10(10): 841-852.

Abstract(1784) PDF(886)

Abstract:
Many engineering problems can be reduced to the solution of a variable coefficient differential equation.In this paper,the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition.By this method,the general computation formal is obtained.Its convergence in proved.We can get analytic expressions which converge to exact solution and its higher order derivatives uniformy Four numerical examples are given,which indicate that satisfactory results can he obtaned by this method.

The Separation of Large Vortexes and the Closed Equations of Turbulence Model

Lin Duo-min, Tsai Shu-tang

1989, 10(10): 853-864.

Abstract(1738) PDF(629)

Abstract:
This paper presents a new kind of everage for the loeally-generated large vortexes so that the physieal quantities of the locally-generated large vortexes and the external large vortexes canberigorously separated from the equal ions for the large vortexes proposed in a previous paper^[1] To the equations for the two kinds of large vortexes,some auxiliary relations are introduced,and the value,of the length-scale l_N of energy dissipation of the external large vortexes may he determined according to the actual circumstances of the disturbance of external sources.Thus the resulting equations of the second moments of turbulent velocity fluctuations for the two kinds of large vortexes can be made closed.Meanwhile,the corresponding coefficients of diffusion in the previous paper^[1] are improved,Finally,a closed set of numerically-solvable equations of turbulence model are obtained.

Finite Element Method Combined with Dynamic Photoelastic Analysis to Determine Dynamic Stress-Intensity Factors

Ning Jie, Chien Wei-zang

1989, 10(10): 865-870.

Abstract(1688) PDF(518)

Abstract:
The present paper is addressed to the finite element method combined with dynamic photoelastic analysis of propagating cracks,that is,on the basis of [1] by Chien Wei-zang,finite elements which incorporate the propagating crack-tip singularity intrinsic to two-dimensional elasticity are employed.The relation between crack opening length and time step obtained from dynamic photoelaslie analysis is used as a definite condition for solving the dynamic equations and simulating the crack propagations as well As an example,the impact response of dynamie-bending-test specimen is investigated and the dynamic stress-intensity factor obtained from the mentioned finite element analysis and dynamic photoelasticity is in reasonable agreement with each other.

Defect and Improvement of Two-Time Expansion Method in Nonlinear Oscillations

Cheng Shui-li, Tan Zhi-min

1989, 10(10): 871-880.

Abstract(1746) PDF(516)

Abstract:
In this paper,the defect of the Two-Time Expansion method is indicated and an improvement of this method is suggested.Certain examples.in which the present method is used,are given.Moreover,the paper shows the equivalence of the improved Two-Time Expansion Method and the method of КВМ(Крылов-Воголюбов-Мигроцолъский)

Reconstruction of Part of an Actual Blast-Wave Flow Field to Agree with Experimental Data by Using Numerical Method with High Identification

Wu Qing-song

1989, 10(10): 881-887.

Abstract(1635) PDF(431)

Abstract:
In this paper,on the basis of experimental data of two kinds of chemical explosions,the piston-pushing model of spherical blast-waves and the second-order Godunov-type scheme of finite difference methods with high identification to discontinuity are used to the numerical reconstruction of part of an actual hemispherical blast-wave flow field by properly adjusting the moving bounary conditions of a piston.This method is simple and reliable.It is suitable to the evaluation of effects of the blast-wave flow field away from the explosion center.

Kinematic Analysis of the General Spatial 7R Mechanism

Chen Wei-rong, Lu Xing-yong

1989, 10(10): 889-900.

Abstract(1887) PDF(498)

Abstract:
The displacement,velocity and acceleration analysis of the general spatial 7R mechanism is discussed in this paper,fused on the method proposed in Ref.[2],an input-output algebra equation of the 16th degree in the tan-half-angle of the output angular displacement is derived.The derivation process and computation are considerably simple.A program written in Allanguage is used to derive the coefficients of displacement equations: therefore the amount of manual work is greatly decreased.The results are verified by a numerical example.The researches of this paper and Ref.[5]found a base for establishing an expert system of spatial mechanism analysis in the future.

The Equations of Motion of a Mechanical System in Matrix Form

R. G. Moukharliamov, Liu Wei-jian

1989, 10(10): 901-908.

Abstract(2098) PDF(511)

Abstract:
This work recommends methods of construction of equations of motion of mechanical systems in matrix form.The use of a matrix form allows one to write an equation of dynamics in compact form,convenient for the in vestigation of multidimensional mechanical systems with the help of computers.Use is made of different methods of constructing equations of motion,based on the basic laws of dynamics as well as on the principles of D'Alambert-Le range,Hamilton-Ostrogradski and Gauss.

The Criterions for Absolute Stability of Direct Control Systems of Lurie Type

Zhang Wei

1989, 10(10): 909-920.

Abstract(1637) PDF(619)

Abstract:
In this paper,we give necessary and sufficient conditions for absolute stability of several classes of direct control systems,and discuss the absolute stability of the first canonical form of control system.The corresponding results in references [3],[5],[6],[7] are improved.

The Boundary Expanding-Contracting Method

Song Shun-cheng

1989, 10(10): 921-928.

Abstract(1876) PDF(530)

Abstract:
The boundary element method(KEM) which a used to solve the elastic problems has more advantages than other numerical methods.Especially,it can resolve rapidly varying internal stress and strain fields more accurately.However,it is of en fails in the region near the boundary because of the singularity of the solutions.Though we can increase the boundary meshes more and more,the solutions of stress on the boundary can't be given directly;which has obstructed the applications of the HEM to some extent.In this paper we proposed the boudary expanding-contracting principle and the boundary expanding-contracting method(BECM) based on the principle.With this method,not only the solutions in the region near or on the boundary can be obtained directly,but the iterative processes can also he used conveniently to improve the accuracy of the solutions.

Transverse Vibration of Rectangular Plates Elastically Supported at Points on Edges

Zhou Ding

1989, 10(10): 929-938.

Abstract(1894) PDF(562)

Abstract:
This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points.The number and location of these points on free edges may be completely arbitrary.This paper uses impulse function to represent reaction and moment at points.Fourter series is used to expand the impulse function along the edges.Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.