应用数学和力学

1995 Vol. 16, No. 3

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1995, 16(3): 189-203.

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Abstract:

On the Closure Problem of Turbulence Model Theory

Cai Shu-tang, Liu Yu-lu

1995, 16(3): 211-215.

Abstract(2378) PDF(790)

Abstract:
It is a wrong viewpoint that the turbulence closure problem is due to the non-linearity,of Navier-stokes equation,But this is a wrong viewed for the closure problem of turbulence model theory.In the engineering,the average raged velocity and pressure are not satisfied,on the other hand,even if the N-Sequation were linear,all of the physical quantities would be found.In this paper,were analysed the closure problem and concluded that the closure problem is induced by lack of statistical distribution function.The limit of turbulence model theory and non-possiblity of direct numerical method to solve the turbulence problem had been paiated out.

Chaotic Behavior of Forced Oscillator Containing a Square Nonlinear Term on Principal Resonance Curves

Pei Qin-yuan, Li Li

1995, 16(3): 217-223.

Abstract(2057) PDF(438)

Abstract:
Based on [1],we investigate the route to chaos in forced oscillator containing a square nonlinear term on principal resonance curves. And chaotic motion is observed against the background of classical resonance curves,stability limits and jump phenomena.It is shown that chaotic motion appears in the neighbourhood of the point both meeting condition that Melnikov function has simple zero and having the point of vertical tangent of the resonance curves.

On the Stability 0f Nonholonomic Mechanical Systems with Respect to Partial Variables

Zhu Hai-ping, Mei Feng-xiang

1995, 16(3): 225-233.

Abstract(2074) PDF(535)

Abstract:
In this paper,a method to study the stability of nonholonomic systems with respect to partial variables is given and several stability theorems of nonholonomic systems with respect to partial variables are obtained. Moreover,a relationship between the stability of a nonholonomic system with respect to all variables and thatto partial variables is obtained.

Samplin9 Formulae of Higher Order

Chen Da-duan, Liu Xiao-ming

1995, 16(3): 235-244.

Abstract(2202) PDF(585)

Abstract:
Shannon sampling theorem is the basic theorem in signal reconstruction based on discrete sampling values in communication theory. The convergence rate of this formula,however,is very slow. Professor Pen Rui-reng. after some slight compromiseon sampling rate,has come to the 3rd order,the 4th order and the 5th order sampling formulae. The calculation of the third order formula on the computer proves that it converges much faster than the Shannon formula. This paper gives a general method to comstruct a higher order sampling formula.

Thermoelasticity Analysis of Finite Composite Laminates Weakened by Multiple Elliptical Holes

Xu Xi-wu, Sun Liang-xin, Fan Xu-qi

1995, 16(3): 245-254.

Abstract(2195) PDF(542)

Abstract:
A finite composite laminate weakened by multiple elliptical holes of arbitrary distribution,arbitrary orientation and arbitrary dimension,is treated as an anisotropic,finite multiple connected thin plate. Using the complex potential method in plane theory of heat conduction and elastictiy of an anisotropic body,the analytical solution of a finite composite laminated plate subjected to arbitrary mechanical and thermal loads with multiple elliptical holes is obtained by means of the Faber series expansion,mapping and the least square boundary collocation technique. The effects of some parameters on the thermostress distribution are studied in detail. Some conclusions are drawn.

The Pansystems View of Prediction and Blow-Up of Fluid

Ouyang Shou-cheng

1995, 16(3): 255-262.

Abstract(2211) PDF(570)

Abstract:
From the pansystems view of prediction,the paper investigates the blow-up andpost blow-up of fluid in rotation and convergence.The results show that the motion includes certain characteristics of reverse transformation,the counter clockwise rotation can be developed into clockwise,and vice versa;the convergence can be changed into divergence and post blow-up,but the divergence will die out continuously.The real forecasting must look this mechanism in the face.Geneally speaking,the forecasting of evolution for fluid can't be considered only as a traditional Cauchy problem.The traditional forecast models should be rediscussed questioningly.

Intial Value Problem for High Dimensional Dynamic Systems

Zhu Chang-jiang

1995, 16(3): 263-266.

Abstract(2393) PDF(466)

Abstract:
In this paper, we prove the existence of the global classical solutions and the uniform stability of the zero solution to the initial value problem for a class of high dimensional dynamic systems which contain the degenerate case.

Variable Structure Control of Indefinite-Dimensional Systems

Li Wen-lin, Bian Wen-ming

1995, 16(3): 267-274.

Abstract(2109) PDF(528)

Abstract:
In lhis paper,we study the variable structure control of indefinite-dimensional control systems with the functional analysis method. The reaching conditions,stability conditions and the approximating conditions of sliding mode,as well as the general form of the variable structure control law are given, and the elementary frame of the variable structure control of indefinite-dimensional systems is built.

An Analytical Solution to Large Deflection Equations of Slmply-Supported Rectangular Hyperboloidal Shallow Shells of Orthotropic Composites

Dong Wen-tang

1995, 16(3): 275-281.

Abstract(2335) PDF(558)

Abstract:
Based on the product rule of the Fourier series and some relevant results inreferences[1,2], a method on solving the large deflection equations of plates and shells by means of the fourier series is proposed in the present paper.Applying this method,we derive a type solution to the Navier's solution of the nonlinear differential equations of the rectangular hyperboloidal shallow shells of the orthotropic composites simply supported.This solution is suitable for plates and shells with large deflection or small deflection whether it is isotropic or orthotropic.Their data processing results are correlative with those found in the classical examples and from the experiments.