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(2451) 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 prof...

Nonlinear Stability of Spherical Shallow Shell under Compound Loads

Yeh Kai-yuan, Liu Ping

1991, 12(1): 11-17.

Abstract(2231) 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 giv...

Higher-Order Melnikov Method

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

1991, 12(1): 19-30.

Abstract(2288) 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...

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(1830) 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 theor...

Absolute Representations of Spins of Principal Frames in a Continuum

Guo Zhong-heng, Liang Hao-yun

1991, 12(1): 39-44.

Abstract(2282) 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(2167) 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...

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(1853) 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 ta...

Research on Haar Spectrum in Fault Diagnosis of Rotating Machinery

Xu Yin-ge, Yan Yu-ling

1991, 12(1): 55-60.

Abstract(1911) 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 approxi...

On the Characteristics of Applied Mathematics

Qin Yuan-xun

1991, 12(1): 61-62.

Abstract(2059) PDF(460)

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(1932) 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,...

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

Lin Zong-chi

1991, 12(1): 69-76.

Abstract(2254) 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 sufficientl...

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

Ding Xie-ping

1991, 12(1): 77-84.

Abstract(2100) 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 t...

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

Zhang Ru-qing

1991, 12(1): 85-90.

Abstract(2466) 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(2166) 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 ...

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

Zhang Han-xin

1991, 12(1): 97-100.

Abstract(2482) PDF(832)

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 sh...