应用数学和力学

1988 Vol. 9, No. 11

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The Initial Post-Buckling Behavior of Ring Stiffened Shells under Hydrostatic Pressure

He Fu-bao, Yu Zhi-meng

1988, 9(11): 951-962.

Abstract(2080) PDF(534)

Abstract:
In this article the initial postbuckling behavior of ring stiffened cylindrical shells under hydrostatic pressure is analyzed by Koiter's theory.The nonlinear bending equations consistent with boundary conditions have been used in prebuckling slate.The eigenvalue problem is solved by Galerkin's method.The obtained buckling loads are compared with the results which are based on classical stability theory.As calculating examples, three typical outside-stiffened cylinders with different ring stiffener parameters are chosen.The results show that the strength of stiffener not only influences buckling load obviously, but also changes the imperfection-sensitivity of cylindrical shells.

Free Vibration of Nonlinear Deformation Ring-and Stringer Stiffened Nonuniform Cylindrical Shell

Ye Kai-yuan, Ji Zhen-yi

1988, 9(11): 963-974.

Abstract(1909) PDF(549)

Abstract:
Cylindrical shells stiffened with rings and stringers are used in many structural application with as pipes conveying fluids or gases and aerospace.In this paper, the eral solulin is obtained for free vibration of nonlinear deformation ring-and stringer-stiffened cylindrical shell with arbitrary boundary condition by step reduction method, Finally, it is only necessary to solve a nonlinearl gebraic equation.This equation is expressed as an analytic form.Its convergence is proved.Three numerical examples are given at the end of the paper which indicate that satisfactory results can he obtained by step reduction method.

Perturbation Method to Solve the Couple Problem among Harmonic Waves

Gao Shi-qiao, Lu Wen-da

1988, 9(11): 975-980.

Abstract(1800) PDF(535)

Abstract:
In this paper, in terms of the characteristics of weak coupling problems between different harmonic waves, a perturbation method was presented to solve the coupling problem among harmonic waves.

Developing Flows and Developed Flows

Cen Ren-jing, Liu Bao-sen

1988, 9(11): 981-992.

Abstract(1854) PDF(546)

Abstract:
This paper puts emphasis on the problem of the developing flows in the circular tube under oscillatory conditions.According to the Navier-Stokes' equation and using the method of Bessel function of imaginary argument, a system of formulas is obtained.Comparing the formulas obtained in this paper with A tabek's formulas, it may be seen that the former is simpler and more convenient.When both the formulas obtained in this paper and A tabek's formulas are reduced to the representation of developed flows, both of them are consistent.Numerical calculation results show that the computed results obtained in this paper are rather consistent with both A tabek's computed results and the experimental results.

A General Analytical Solution for Elastic Vibration of Rectangular Thin Plates

Huang Yan

1988, 9(11): 993-1000.

Abstract(1849) PDF(571)

Abstract:
A general solution of differential equation for lateral displacement lunction of rectangular elastic thin plates in free vibration ix established in this paper.It can be used to solve the vibration problem of rectangular plate with arbitrary boundaries.As an example, the frequency and its vibration mode of a rectangular plate with jour edges free have been solved.

The Global Structural Stability and Application of the Toroidal Differential Equations

Zhou Rong-xing

1988, 9(11): 1001-1013.

Abstract(2090) PDF(455)

Abstract:
In this paper, the global structural stability of the toroidal differential equations has been obtained, and applied to the cross-coupled phase -locked loop, where Δω≥0.

The End and Spacing Effect of Induction Coil of Finite Length on the EM Field in HF Plasma

Tang Fu-lin, Chen Yun-ming

1988, 9(11): 1015-1022.

Abstract(1941) PDF(463)

Abstract:
In practical applications the diameter and height of the induction coil have the same order of magnitude, hence the end effect is unnegligible in Iff(high frequency) plasma theory.The present paper calculates the electromagnetic field under the assumption of infinite plasma column with uniform conductivity.The results show that the magnetic induction differs greatly from that in vacuum case at axis, and even the direction is reversed in some cases.In contrast, the difference is not large at plasma surface, and the,phase lag between B and E there changes little, either.Hence, the EM field at the surface in vacuum case can be more adequately applied as boundary condition in HF plasma computation.

On Discrete Supports and Continued Support of Structures

Wang Shu

1988, 9(11): 1023-1032.

Abstract(2111) PDF(481)

Abstract:
There have been several papers dealing with elastic discrete supports of structures.And we are interested in what relation there is between elastic discrete supports and continued support and what difference would result in for dynamic properties of structures under the two kinds of supports.Through the present analysis, it is pointed out that natural frequencies reflect a certain proportion of kinetic and potential energies in total energy of a system, and the frequencies can be guaranteed to be invariable in transforming between elastic discrete and continued supports by means of a proper energy equivalence.And the theoretical formulation of beams and numerical results of shells of revolution are presented in this paper.

A Criterion for the Stability of Motion of Nonlinear Systems

Zhao Jun-san

1988, 9(11): 1033-1036.

Abstract(2115) PDF(464)

Abstract:
As to an autonomous nonlinear system, the stability of the equilibrium slate in a sufficiently small neighborhood of the equilibrium state can be determined by eigen values of the linear pan of the nonlinear system provided that the eigenvalues are not in a critical case.Many methods may be used to detect the stability for a linear system.A lot of researches for determining the stability of a nonlinear system are completed by mathematicians and mechanicians but most of them are methods for the special forms of nonlinear systems.Till now.none of these methods can be conveniently applied to all nonlinear systems.The method introduced by this paper gives the necessary and sufficient conditions of the stability of a nonlinear system.The familiar Krasoyski's method is a special case of this method^[1],[2].

Calculation of Conformal Mapping Function of the Tooth Profile on Evolvent Gear by Computer

Cheng Nai-shi, Liu Wen

1988, 9(11): 1037-1044.

Abstract(2483) PDF(560)

Abstract:
The exact solution of the stress and the displacement on spur gear can be gained by the method of con formal mapping of complex variables in plane elasticity.But it is difficult to get the comformal mapping function for the tooth profile with different parameters.They used to be obtained through trial method.This is time-consuming and expensive.In this paper a computer program is drawn up for the conformal mapping function.A large amount of calculation has given proof of its success and of the precision of the mapping function: thereby the main obstacle has been removed for the practical application of the conformal mapping method to the stress and displacement of tooth on evolvent gear.