应用数学和力学

1990 Vol. 11, No. 8

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The Double and Triple Velocity Correlations of Small Vortexes in Three-Vortex Model Theory and the Decay of Grid Produced Turbulence

Lin Duo-min, Cai Shu-tang

1990, 11(8): 659-664.

Abstract(1785) PDF(493)

Abstract:
In the three-vortex model theory of turbulence^[1,2] and double and the triple velocity correlation functions of small vortexes were employed. In this paper, the double and the triple velocity correlation functions of small vortexes are further discussed, and the expressions of some coefficients in t...

Numerical Solution of the Singularly Perturbed Problem for the Hyperbolic Equation with Initial Jump

Su Yu-cheng, Lin Ping

1990, 11(8): 665-670.

Abstract(1746) PDF(493)

Abstract:
In this paper we consider the initial-boundary value problem for a second order hyperbolic equation with initial jump. The bounds on the derivatives of the exact solution are given. Then a difference scheme is constructed on a non-uniform grid. Finally, uniform convergence of the difference solution...

Stress Intensity Factors of a Plate with Two Cracks Emanating from an Arbitrary Hole

Wang Yuan-han

1990, 11(8): 677-686.

Abstract(1977) PDF(552)

Abstract:
In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculated examples include a circular, elliptical, rectangular, or rhombic hole in a plate....

Analysis of Surface Crack on Forward Extruding Bar during Axisymmetric Cup-Bar Combined Extrusion Process

Li Miao-quan, Wu Shi-chun, Tang Cai-rong

1990, 11(8): 687-695.

Abstract(1843) PDF(454)

Abstract:
In this paper, the kinematically admissible velocity field with surface crack on forward extruding bar is put forward during the axisymmetric cup-bar combined extrusion process, in accordance with the results of model experiments.On the basis of velocity field, the necessary condition for surface cr...

Extraction of Characteristic Roots on BesseLl-Neumann’s Mixed Equations

Yang Wen-xiong, Gu Er-zuo, Zhu Min

1990, 11(8): 705-712.

Abstract(1895) PDF(419)

Abstract:
This paper discusses the problem of the extraction of characteristic roots {λ_t}(λ₀<λ₁<λ₂…) on Bessel-Neumann's mixed equations. It gives the expressions and the evaluation of the minimum root. The advantage of the method has no use for the table of the multi-figure number Bessel function and i...

The Integral as a Function of the Upper Limit and an Analytical Solution to Plane Strain Drawing and Extrusion

Zhao De-wen, Zhao Zhi-ye, Zhang Qiang

1990, 11(8): 713-718.

Abstract(2000) PDF(545)

Abstract:
A kinematically admissible velocity field which is different from Avitzur's is established in Cartesian Coordinates. An upper-bound analytical solution to strip drawing andextrusion is obtained by using the integral as a function of the upper limit in this paper.

Fuzzy Cluster Analysis of Turbulent Scales

Liang Zai-chao Liu Shi-he

1990, 11(8): 719-724.

Abstract(1882) PDF(450)

Abstract:
Turbulent motion could be regarded as the superposition of fluctuations with different scales. It's of great theoretical and practical importance to determine the classification of turbulent scales quantitatively to the better description of vortex motions with different scales, and to the research ...

Noise at Inception and Collapse of a Cavity

Huang Jing-chuan

1990, 11(8): 725-730.

Abstract(1889) PDF(640)

Abstract:
The paper analyzes the noise at inception and collapse of an isolated bubble cavity filled with gas and vapour. The expressions and their numerical solutions of the sound pressure and the vibration velocity are presented.The results indicate that the noise occurs at every stage of a cavity. The nois...

Stability of Nonlinear Comparison Equations for Discrete Large-Scale Systems

Shu Huang

1990, 11(8): 731-737.

Abstract(1788) PDF(449)

Abstract:
On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability ...

Some Properties of Far Field Patterns of Acoustic Waves in an lnhomogeneous Medium

Cheng Jin

1990, 11(8): 739-746.

Abstract(1785) PDF(428)

Abstract:
In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.

On the Limit Case of the Step-Reduction Method for Calculating Non Uniform Beam with Various Sections

Wu Jiong-yu

1990, 11(8): 747-752.

Abstract(1927) PDF(541)

Abstract:
In this paper, the step reduction method is discussed, which was advanced by Prof, Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the inf...

A Series Boundary Integration Method for the Bending Analysis of Anisotropic Plates

Liang Li-ping

1990, 11(8): 897-704.

Abstract(1837) PDF(611)

Abstract:
A series boundary integration method is given which exactly satisfies the fundamental equation of bending analysis of general anisotropic plates or laminated plates in Kirchhoffs sense. With a unified deflection series, the method may be applied to the plates having different planforms and support c...