应用数学和力学

Lagrange Equation of Another Class of Nonholonomic Systems

Gao Pu-yun, Guo Zhong-heng

1991, 12(8): 679-684.

Abstract(2162) PDF(448)

Abstract:
Using the method of [1], the present paper derives the Lagrange equation without multipliers for another class of first-order nonholonomic dynamical systems by means of variational principle. This kind of equations is also new.

Numerical Methods for Parabolic Equation with a Small Parameter in Time Variable

Wu Qi-guang, Li Ji-chun

1991, 12(8): 685-691.

Abstract(1966) PDF(588)

Abstract:
In this paper, we discuss the parabolic equation with a small parameter on the derivative in time variable. We construct difference scheme on the non-uniform mesh according to Bakhvalov, and prove the one-order uniform convergence of this scheme. Numerical results are presented.

Maximal Elements of Condensing Preference Maps in Locally Convex Hausdorff Spaces

Ding Xie-ping

1991, 12(8): 693-696.

Abstract(2253) PDF(503)

Abstract:
Two existence theorems of maximal elements of condensing preference maps in locally convex Hausdorff spaces are proved which generalize the recent results of Mehta. One of them positively answers the open problem mentioned by Mehta.

The Application of Pattern Recognition Techniques in Fault Diagnosis of Machinery Equipment

Yan Yu-ling, Xu Yin-ge

1991, 12(8): 697-701.

Abstract(2013) PDF(488)

Abstract:
In this paper, the characteristics of vibration signal of machinery in different running conditions are statistically analysed, and some moments of statistical distribution of signals are selected as the eigenvector to condense the state information. Here, we divide the states of machinery into two:‘good' and ‘faulty', and the pattern recognition techniques are used to classify the running conditions of machinery. At the end of this paper, the authors present some test data, and from the results obtained, it's verified that the eigenvector selected is reliable and sensible to faults. And the results also show the effectiveness of classification rule.

Numerical Solution of a Nonlinear Reaction-Diffusion Equation

Tang Shi-min, Qin Su-di, R. O. Weber

1991, 12(8): 703-709.

Abstract(2209) PDF(556)

Abstract:
A nonlinear reaction-diffusion equation is studied numerically by a Petrov-Galerkin finite element method, which has been proved to be 2nd-order accurate in time and 4th-order in space. The comparison between the exact and numerical solutions of progressive waves shows that this numerical scheme is quite accurate, stable andefflcient. It is also shown that any local disturbance will spread, have a full growth and finally form two progressive waves propagating in both directions. The shape and the speed of the long term progressive waves are determined by the system itself, and do not depend on the details of the initial values.

Aerodynamic Analysis of Circular Plate-Shaped and Circular Ring-Shaped Squeeze Film Bearings

Yao De-liang, Fu Xian-luo

1991, 12(8): 711-718.

Abstract(1907) PDF(478)

Abstract:
Aerodynamics of circular plate- and circular ring-shaped squeeze film hearings is analyzed in detail, yielding analytic expressions for the pressure distribution of these hearings. Several formulae for these hearings are modified using the developed method. The paper also gives numerical results oj pressure distribution and load-hearing capacities of these hearings.

A New IVIatrix Perturbation Method for Analytical Solution of the Complex Modal Eigenvalue Problem of Viscously Damped Linear Vibration Systems

Lü Zhen-hua, Feng Zhen-dong, Fang Chuan-liu

1991, 12(8): 719-728.

Abstract(2847) PDF(1118)

Abstract:
A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional- and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.

A Calculating Method of Shock Wave Oscillating Frequency Due to Turbulent Shear Layer Fluctuations in Supersonic Flow

Xu Li-gong, Ran Zheng

1991, 12(8): 729-735.

Abstract(2401) PDF(553)

Abstract:
One of the more severe fluctuating pressure environments encountered in supersonic or hypersonic flows is the shock wave oscillation driven by interaction of a shock wave with boundary layer. The high intensity oscillating shock wave may induce structure resonance of a high speed vehicle. The research for the shock oscillation used to adopt empirical or semiempirical methods because the phenomenon is very complex. In this paper a theoretical solution on shock oscillating frequency due to turbulent shear layer fluctuations has been obtained from basic conservation equations. Moreover, we have attained the regularity of the frequency of oscillating shock varying with incoming flow Much numbers M_∞ and turning angle θ. The calculating results indicate excellent agreement with measurements. This paper has supplied a valuable analytical method to study aeroelastic problems produced by shock wave oscillation.

Buckling and Post-Buckling of Annular Plates on an Elastic Foundation

Yang Xiao, Cheng Chang-jun

1991, 12(8): 737-748.

Abstract(2392) PDF(540)

Abstract:
On the basis of von Kámán nequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting.

One Type of Integrals for the Equations of Motion of Higher-Order Nonholonomic Systems

Mei Feng-xiang

1991, 12(8): 749-756.

Abstract(1970) PDF(529)

Abstract:
This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and p-order integral (p>2)All of these integrals can be constructed by the Lagrangian function of the system. Two examples are given to illustrate the application of the suggested method.

Deformation of Structure and Spectrum of Evolution Equations

Xie Han-guang

1991, 12(8): 757-760.

Abstract(1988) PDF(472)

Abstract:
In this paper, we study the general structure of evolution equations of the AKNS eigenvalue problem q(x,t), r(x,t) with the spectrum varying as and A₁,B₁,C₁are all positive or negative power polynomials of where q, r are not limited with any additional conditions at infinity.

Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter

Pan Zhong-xiong, Wang Yi-fei

1991, 12(8): 761-767.

Abstract(1698) PDF(597)

Abstract:
This paper deals with the numerical method for the system of reaction-diffusion equations with a small parameter. It is difficult to solve the problems of this kind numerically because of the boundary layer efect Besed on singular perturbed theory and Greens function, we have established the difference scheme that is suited for the solution to the problems. We introduce an idea of feasitbe equidistant degree a here. And this proves that if a≥2 the scheme converges in norm with speed O(h+Δt) uniformly.

1991 Vol. 12, No. 8