应用数学和力学

1986 Vol. 7, No. 9

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Equi-Strength Design of Nonhomogeneous Variable Thickness High Speed Rotating Disk under Steady Temperature Field

Yhe Kai-yuan, Liu Ping

1986, 7(9): 769-778.

Abstract(2136) PDF(702)

Abstract:
Considering the mutual interaction between the thickness of the disk and temperature distribution,and directly using results in [1],[2] and the iteration method suggested in this paper,we obtain the equi-strength thickness distribution of nonhomogeneous variable thickness high speed rotating disk under axisymmetrical steady temperature field.

The Fundamental Equations of Two-Dimensional Layer Flows

Tsai Shu-tang, Wu Feng

1986, 7(9): 779-784.

Abstract(1954) PDF(579)

Abstract:
In many studies on two-dimensional flows in field of atmosphere and ocean the equations which are extension of river-hydraulic equations or Navier-Stokes equations are usually used.In these equations stand for turbulent resistance.Obviously use of these equations in practice may lead to contradiction.In this paper the average of Reynolds equations over depth is taken.The motion equations,continuity equation and diffusion equation are obtained for the average physical variables.

Several Criterions of Absolute Stability for the Second Canonical Form of Control System

Qiu Xiao-gang, Shu Zhong-zhou

1986, 7(9): 785-800.

Abstract(2066) PDF(632)

Abstract:
In this paper,several explicit criterions of absolute stability for the real second canonical form of control system are given,which generalize and include the known result in ref.[2].By applying these criterions to the well known equations of the longitudinal motion of aircraft,a result that generalizes and includes the known results in refs.[3,4,2] is obtained.

Solutions of Magnetohydrodynamics Equations——The Theory of Functions of a Complex Variable under Dirac-Pauli Representation and Its Application in Fluid Dynamics(IV)

Shen Hui-chuan

1986, 7(9): 801-811.

Abstract(2646) PDF(1021)

Abstract:
This work is the continuation of the discussion of Refs.[1 3],(i) We turn the Magnetohydrodynamics equations of isentropic compressible and non-dissipative magneto-flow into the form of the ideal hydrodynamics equations in this paper; we can obtain the general Chaplygin equation from Ref.[3],and the general sduction of this equation.(ii) We apply the theory of functions of a complex rariable under Dirac-pauli representation,turn the general Magnetohydrodynamics equations of incompressible mageto-flow into two nonlinear equations for flow function and "magneto-flow function",and obtain the exact stable solution of incompressible magnetohydrodynamics equations under the condition of stable magnetic field(i.e.under conditon of equality for kinematical viscid coefficient or viscid diffusion coefficient with magnetic diffusion coefficient).

Free Bending Vibration of Elliptical Column Partially Submerged in Water

Zhang Xi-de, Zhang Wen

1986, 7(9): 813-820.

Abstract(2237) PDF(493)

Abstract:
This paper studies the free bending vibration of elliptical column partialy submerged in water.It is the first time that we get an exact solution of the function of normal mode of vibretion of column-water couple system and a corresponding frequency equation denoted by limited order determinant.It points out that the effect of water is equivalent to an attached distributive mass.Therefore,the frequency with water is lower than that without water.

To Solve the Shallow Shell Equations with the Help of the Plate’s Equation Solution(Lowering the Order of Partial Differential Equation from 8 to 2)

Fan Jia-shen

1986, 7(9): 821-830.

Abstract(2099) PDF(501)

Abstract:
If a plate solution is known which has the same boundary and loading conditions with a shallow shell,the solution of that shell can be reduced to a non-homogeneous Helmholtz's equation in complex domain.Two examples are given to illustrate our method.

Reliability Growth for Multi-System Simultaneous Development

Zhou Yuan-quan

1986, 7(9): 831-837.

Abstract(2100) PDF(581)

Abstract:
In this paper the AMSAA model for multi-system simultaneous development is discussed.The maximum likelihood(ML) estimates of the parameters and the confidence intervals of the MTBF for Weibull process are presented.Crow's formulae^[1] are the special examples for this paper.

Measurements for Dynamic Deformation by Mismatch with Speckle Method

Chen Fang, Cao Zheng-yuan, Fang Ru-hua, Chen Ping-ping

1986, 7(9): 839-846.

Abstract(2553) PDF(667)

Abstract:
This paper presents a simple method for measurements,of dynamic deformation by mismatch white speckle method using dynamic photoelastic device.The method is able to measure not only large dynamic deformation^[1],but also small dynamic deformation.Combined with dynamic isochromate pattern,the elastic modulus Poisson's ratio and dynamic material fringe value of the material measured can be obtained by the method.

The Differentia, Geometric Principle of the Nonholonomic Mechanical Systems of Chetaev’s Type

Zhao Shi-ying

1986, 7(9): 847-860.

Abstract(2259) PDF(1030)

Abstract:
This paper deals with the nonholonomic mechanical systems of Chetaev's type by use of modern differential geometric methods.Based on a precise definition of Chetaev-type constraint pfaffian systems,the differential geometric structure is given for the description of nonholonomic mechanical systems.In thisframwork,the classical theory of Lagrange's equations with nonholonomic constraints is put into an invariant and coordinate free form.Furthermore,the problems of constraint imbedding and conservation laws are discussed within thisframwork,and the Noether-type thereom on constraint-imbedding submanifolds is obtained.

The Leakage Criterions of Thin-Wall Pressure Vessels,Materials of Missile and Spacecraft

Wang Xing-fa

1986, 7(9): 861-866.

Abstract(1830) PDF(462)

Abstract:
This paper presents the development of three leadage cr Her ions to predict fracture in thin-wall pressure vessels,materials of missile and spaceraft.Experimental results show that the.criterions are successful.