应用数学和力学

1991 Vol. 12, No. 1

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The Numerical Simulation of Turbulent Flows of Newtonian and a Sort of Non-Newtonian Fluid in 180-Degree Square Sectioned Bend

Feng Tong, Chien wei-zang, Sun Hou-jun

1991, 12(1): 1-10.

Abstract(2277) PDF(481)

Abstract:
Using k-ε model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulated numerically. The calculated results agreed well with the measured velocity profiles. On the basis of calculation and measurement, appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.

Nonlinear Stability of Spherical Shallow Shell under Compound Loads

Yeh Kai-yuan, Liu Ping

1991, 12(1): 11-17.

Abstract(2115) PDF(455)

Abstract:
Using a semi-analytical method, the nonlinear stability of a spherical shallow shell under centrally distributed and concentrated loads is investigated in this paper. The longer manual calculation has been avoided when finding the approximate solution, and the P-W_m characteristic relation can be given analytically.

Higher-Order Melnikov Method

Guo You-zhong, Liu Zeng-rong, Jiang Xia-mei, Han Zhi-bin

1991, 12(1): 19-30.

Abstract(2154) PDF(518)

Abstract:
In this paper the Melnikoy method has been generalized to the case of higher-order by finding an explicit expression for second-order subharmonic Melnikov function, and it has been proved that the existence of subharmonic or hyper-subharmonic of a system can be proved under certain conditions by use of second-order Melnikov function.

Some Existence Theorems of Common and Coincidence Solutions for a Class of Functional Equations Arising in Dynamic Programming

Zhang Shi-sheng

1991, 12(1): 31-37.

Abstract(1735) PDF(475)

Abstract:
Same existence theorems of common and coincidence solutions for a class of more general systems of functional equations arising in dynamic programming are shown. The results presented in this paper not only contain the corresponding results of [6,7] as special cases, hut also give an existence theorem of solutions for a class of functional equations suggested by Wang^[2,5] recently.

Absolute Representations of Spins of Principal Frames in a Continuum

Guo Zhong-heng, Liang Hao-yun

1991, 12(1): 39-44.

Abstract(2141) PDF(421)

Abstract:
The presem paper offers a general me thod to find the absolute expressions for different spins in a continuum for which only "the principal axis expressions" were available, and in this way it makes the further applications of these spins possible.

On the Computation of the Main Eigen-Pairs of the Continuous-Time Linear Quadratic Control Problem

Zhong Wan-xie, Yang Zai-shi

1991, 12(1): 45-50.

Abstract(2044) PDF(623)

Abstract:
The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt→0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has bee ft reduced from the original In-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation A_e=e^A.All the eigenvalues of A_e are in the unit circle, with the eigenvectors unchanged and the original eigenvalues can be obtained by a logarithm operation. And several of the eigenvalues of A_e nearest to the unit circle can be calculated by the dual subspace iteration method.

Large Deflection Analysis of Rectangular Plates by Combined Perturbation and Finite Strip Method

Su Xu-min, Zhao Zu-wu

1991, 12(1): 51-54.

Abstract(1711) PDF(475)

Abstract:
The perturbation method and finite strip method are combined to solve the large deflection bending problems of rectangular plates. Perturbation method is used to reduce the nonlinear differential equations into a series of linear differential equations. The finite strip method is then employed to tackle these linear equations. Some calculation examples are compared with those got by other methods.

Research on Haar Spectrum in Fault Diagnosis of Rotating Machinery

Xu Yin-ge, Yan Yu-ling

1991, 12(1): 55-60.

Abstract(1801) PDF(423)

Abstract:
In this paper, Haar Transform (HT) is used in the fault diagnosis of rotating machinery, and the "Impulse Sharpness" is presented as a diagnostic index. At present, Fourier Spectrumanalysis is most widely used. Compared with FFT, HT is more rapid in computation and more effective in discrete approximation. It's very suitable for the extraction of pulses in the signal. However, HT has some shortcomings. It's greatly affected by the starting point and length of the sample. Here, the authors present a method to improve the stability and comparability of Haar Spectrum. The fault imitating test of rolling bearing is carried out, and the results obtained have verified the sensitivity of Haar Spectrum and Impulse Index to the fault.

On the Characteristics of Applied Mathematics

Qin Yuan-xun

1991, 12(1): 61-62.

Abstract(1951) PDF(458)

Abstract:
In this paper, four aspects of particular characteristics of Applied Mathematics different from those of Pure Mathematics are summarised by comparison.

Investigation and Applications of Pansystems Recognition Theory and Pansystems-Operations Research of Large-Scale Systems(Ⅱ)

Wu Xue-mou, Guo Ding-he

1991, 12(1): 63-67.

Abstract(1824) PDF(412)

Abstract:
Forming a connecting link between what goes before and comes after, this paper summarizes the general framework of pansystems methodology and related mathematical modelling of fundamental concepts including generalized systems, structure, function, entirety principle of system, pansystems relations, pantransformations, panderivatives, pansymmetries, generalized quantization, etc.

Singular Perturbation of the Fourth Order Elliptic Equation When the Limit Equation Is Elliptic-Parabolic

Lin Zong-chi

1991, 12(1): 69-76.

Abstract(2127) PDF(511)

Abstract:
In this paper we cosider the singular perturbation of the fourth order elliptic equation-ε²Δ²u+y^m∂²u/∂y²+∂²u/∂x²+a(x,y)∂u/∂y+b(x,y)∂u/∂x+c(x,y)=0 when the limit equationis elliptic-parabolic, where ε is a positive parameter, Δ is a positive real number, A is Laplacian operator, a,b,c are sufficiently smooth. Under appropriate condition we derive the sufficient condition of solvability and prove the existence of solution and give a uniformly valid asymptotic solution of arbitrary order.

Intersection Theorems Concerning Noncompact Sets with H-Convex Sections and Their Applications

Ding Xie-ping

1991, 12(1): 77-84.

Abstract(1963) PDF(471)

Abstract:
In this paper, we prove some intersection theorems concerning noncompact sets with H-convex sections which generalize the corresponding results of Ma, Fan, Tarafdar, Lassonde and Shin-Tan to H-spaces without the linear structure and to noncompact setting. An application to von Neumann type minimax theorems is given.

Parallel Computational Algorithm of Substructure Method of Large-Scale Structure Analysis

Zhang Ru-qing

1991, 12(1): 85-90.

Abstract(2335) PDF(478)

Abstract:
In this paper, according to the parallel environment of ELXSI computer, a parallel solving process of substructure method in static and dynamic analyses of large-scale and complex structure has been put forward, and the corresponding parallel computational program has been developed.

A Note on a New Theory of Turbulence

Tsai Shu-tang, Lin Duo-min

1991, 12(1): 91-95.

Abstract(2039) PDF(406)

Abstract:
In this paper, the creation and annihilation of turbulent eddies are described as elementary particles in the quantum field theory. An elementary particle mav be considered as a solid entity as it exists in quantum theory, but a turbulent eddy is often changed in size and shape with time due to its energy dissipation in a turbulent field. Therefore, in order to apply the method of the quantum field theory to the turbulent field by analogy, the entity of the same eddy should be defined firstly According to the linearized theory, the turbulent eddies with the similarity character in time duration may be considered as the entity of the same eddy, and the creation and annihilation of turbulent eddies without the similar characters are related to the interaction term φ_i in equation (2.6). Then, the creation operator and annihilation operator similar-to those in the quantum field theory are used to describe the state of turbulent eddy field. Finally, a "Schrödinger" equation of turbulent eddies is formulated based upon the nonlinear terms in the original N-S equation. Thus, a new turbulent eddy interaction theory similar to the quantum field theory is obtained.

Implicit, Non-Oscillatory Containing No Free Parameters and Dissipative (INND) Scheme

Zhang Han-xin

1991, 12(1): 97-100.

Abstract(2328) PDF(831)

Abstract:
An implicit non-oscillatory containing no free parameter and dissipative (INND) scheme wiring Navier Stokes equations is developed. This scheme is one of total variation diminishing (TVD) algorithms. The results show that this seheme is applicable for solving Navier Stokes equations, and that the shock-capturing capahilhility and the convergence rate arc satisfactory.