应用数学和力学

1999 Vol. 20, No. 1

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A Coupling Model for Terrestrial Processes in Arid Areas and Its Application

Li Jiachun, Yao Deliang, Sheng Weiming, Xie Zhengtong

1999, 20(1): 1-10.

Abstract(1996) PDF(543)

Abstract:
In this paper, the importance of investigation on terrestrical processes in arid areas for mankind's living environment protection and local economics development as well as its present state of the art are elucidated. A coupling model, which evaluates heat, mass, momentum and radiative fluxes in the SPAC system, is developed for simulating microclimate over plant and bare soil. Especially,It is focussed on the details of turbulence transfer. For illustration, numerical simulation of the water-heat exchange processes at Shapotou Observatory, CAS, Ninxia Province are conducted, and the computational results show that the laws of land-surface processes are rather typical in the arid areas.

Elasticity Solutions for a Piezoelectric Cone Under Concentrated Loads at Its Apex

Ding Haojiang, Guo Fenglin, Zou Daoqin

1999, 20(1): 11-15.

Abstract(2067) PDF(660)

Abstract:
Based on the general solution of the three-dimensional problem for piezoelectric materials, the problem of a piezoelectric cone subjected to concentrated loads at its apex is solved by trial-and-error method. The displacements and stresses are explicitly given for the cases of compression in the presence of point charge, bending and torsion. These solutions are simple in form and convenient for application. When the apex angle 2α equals π, the solutions for concentrated force, point charge and torsion reduce to those of the half-space problem.

Influence of Compression-Bending Coupling on the Stability Behavior of Anisotropic Laminated Panels

Huang Xiaoqing, Zhang Hong

1999, 20(1): 17-24.

Abstract(1964) PDF(575)

Abstract:
Dynamic-Relaxation Method (DRM) is applied to studying the influence of compression-bending coupling on nonlinear behavior of cylindrically slightly curved panels of unsymmetric laminated composite materials subjected to uniform uniaxial compression during loading and unloading. Numerical results are given for cross-ply plates and panels under S4S4 and S4S2 boundary conditions. The results show that the effects of absolute value and the sign of the coupling coefficient on the stability behavior of the panels are significant.

Transient Pressure of Percolation Through One Dimension Porous Media with Threshold Pressure Gradient

Song Fuquan, Liu Ciqun, Li Fanhua

1999, 20(1): 25-32.

Abstract(2601) PDF(760)

Abstract:
This paper studies the transient pressure of percolation during one production and one shutting in one dimension porous media with threshold pressure gradient. The differential equations are derived and solved with numerical computation. Basing on numerical solution, It is analyzed that:1.the relation between the steady pressure at well bore (or at endpoint) and threshold pressure gradient shut-in time, and the correspondent formulae are derived;2.the regulation of transient pressure peak. The result is very useful and will help experiments and applications in development of the low permeadility reservoir with threshold pressure gradient.

Uniqueness of Solution of Field Point of Singular Source Outside-Region-Distribution Method

Yun Tianquan

1999, 20(1): 33-38.

Abstract(2166) PDF(503)

Abstract:
The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outside-region-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing and an integral inequality. Examples of part of these singular sources such as Kelvin's point force, Point-Ring-Couple (PRC) etc. are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.

Simulation of Typhoon’s Anomalous Track (Ⅱ)——CD Method

Lin Mian, Li Jiachun

1999, 20(1): 39-45.

Abstract(2369) PDF(685)

Abstract:
Contour dynamics (CD) method for the motions of typhoon is presented in this paper. The effect of asymmetric inner structure on the typhoon's anomalous track has been discussed in different environmental steering. To demonstrate the feasibility of the method, the track of Typhoon Yancy (9012) is concerned with. The numerical results show that the method can describe the tendency of looping qualitatively.

A Exact Solution of Crack Problems in Piezoelectric Materials

Gao Cunfa, Fan Weixun

1999, 20(1): 47-54.

Abstract(2561) PDF(721)

Abstract:
An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that:(ⅰ) the stress intensity factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ⅱ) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i e, it is always positive, and independent of the electric loads. (ⅲ) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.

Equations of Motion for Nonholonomic Mechanical Systems with Unilateral Constraints

Zhang Yi, Mei Fengxiang

1999, 20(1): 55-62.

Abstract(2508) PDF(606)

Abstract:
In this paper, the equations of motion for nonholonomic mechanicalsystem with unilateral holonomic constraints and unilateral nonholonomic constrains are presented, and an example to illustrate the application of the result is given.

Strongly Resonant Bifurcations of Nonlinearly Coupled Van der Pol-Duffing Oscillator

Gan Chunbiao, Lu Qishao, Huang Kelei

1999, 20(1): 63-70.

Abstract(2342) PDF(678)

Abstract:
In this paper, the strongly resonant bifurcations of a nonlinear coupled Van der Pol-Duffing Oscillator by the classical multi-scale method are studied. It is shown that there exit periodic motions of a single oscillator,frequency-locking and quasi-periodic motions of two oscillators when the parameters vary. Meanwhile, some numerical results are given to test the theoretical ones.

Improvement on Stability and Convergence of A. D. I. Schemes

Cheng Aijie

1999, 20(1): 71-78.

Abstract(2548) PDF(1255)

Abstract:
Alternating direction implicit(A. D. I.)schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form ∂_u/∂_t-∂/∂_x[a(x,y,t)∂_u/∂x-∂/∂_y^o[nb(x,y,t)∂u/∂_y^cs]B=f Two A. D. I. schemes, Peaceman-Rachford scheme and Douglas scheme will be studied. In the literature, stability and convergence have been analysed with Fourier Method, which cannot be extended beyond the model problem with constant coefficients. Additionally, L² energy method has been introduced to analyse the case of non-constant coefficients, however, the conclusions are too weak and incomplete because of the so-called "equiverlence between L² norm and H¹ semi-norm". In this paper, we try to improve these conclusions by H¹ energy estimating method. The principal results are that both of the two A. D. I. schemes are absolutely stable and converge to the exact solution with error estimations O(Δt²＋h²) in discrete H¹ norm. This implies essential improvement of existing conclusions.

The Fractal Research and Predicating on the Time Series of Sunspot Relative Number

Gu Shenshi, Wang Zhiqian, Cheng Jitai

1999, 20(1): 79-84.

Abstract(3070) PDF(1074)

Abstract:
In this paper, with the theory of nonlinear dynamic systems, It is analyzed that the dynamic behavior and the predictability for the monthly mean variations of the sunspot relative number recorded from January 1891 to December 1996. In the progress, the fractal dimension (D=3.3±0.2) for the variation process was computed. This helped us to determine the embedded dimension [2×D＋1]=7. By computing the Lyapunov index (λ₁=0.863), it was indicated that the variation process is a chaotic system. The Kolmogorov entropy (K=0.0260) was also computed, which provides, theoretically, the predicable time scale. And at the end, according to the result of the analysis above, an experimental predication is maded, whose date was a part cut from the sample date.

Modeling of Stochastic Modulated Rattling System

Feng Qi

1999, 20(1): 85-92.

Abstract(2046) PDF(674)

Abstract:
Rattling vibration is an important noise source of gear-box. To control that noise, it is necessary to elaborate a mathematics-mechanical model on rattling gears. In this paper, a rattling system modulated by noise was investigated. Instead of performing the very tedious numerical calculation, a discrete stochastic model described by three dimensional mean mapping was established by means of the Non-Gaussian closure technique. Through the example, the chaotic stochastic behavio may be revealed. In comparsion with deterministic model, the model developed in this paper is more approximate to practice and more availlable for acoustic investigation, so that it is suggested to be applied to modeling on rattling vibratio.

Iterative Approximation with Errors of Fixed Point for a Class of Nonlinear Operation with a Bounder Range

Xue Zhiqun, Zhou Haiyun

1999, 20(1): 93-98.

Abstract(2500) PDF(826)

Abstract:
Let X be a uniformly smooth real Banach space. Let T:X→X be a continuous and strongly accretive operator. For a given ∀f∈X,define S:X_x→X,for all ∀x∈X,Let {α_n}_n^∞=0 be two real sequences in(0,1) satisfying:(ⅰ)α_n→0,β_n→0(n→∞);.Assume that {u_n}_n^∞=0 and {v_n}_n^∞=0 are two sequences in X satisfying ‖un‖= o (A_n) and ‖v_n‖→0 as n→∞].For arbitrary x₀∈X, the iteration sequence {x_n} is defined by Moreover, suppose that {S_nx_n} and {Sy_n} are bounded, then {x_n} converges strongly to the unique fixed point of S.

Radial Vibrations of Axisymmetrically Loaded Stepped Pressure Vessels

Zhang Yingshi, Ma Zhixang

1999, 20(1): 99-103.

Abstract(2044) PDF(540)

Abstract:
Differential equations of free/forced radial vibrations of axisymmetrically loaded stapped pressure vessels are established by using singular functions. Furthermore,their general solutions are solved, the expression of vibration mode function and frequency equations on usual supports are derived with W operator and forced response of such vessels are calculate.

New Results of Some Existence Theorems on Nonlinear Boundary Value Problems

Wu Guangrong, Huang Wenhua, Shen Zuhe

1999, 20(1): 105-109.

Abstract(2168) PDF(612)

Abstract:
With the use of the homeomorohism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, which generalizes results of Brown. When our results are applied to the existence and uniqueness of periodic solutions for nonlinear perturbed conservative systems (Newtonian equations of motion), the existence and uniqueness of the solution obtained. The results in this note seem less restrictive than those of the former papers we have seen. Mean while, as far as we know, it seems that applying the homeomorphism theory to the research of this kind of problem is new.