应用数学和力学

Tsai Shu-tang, Ma Bai-kun

1987, 8(4): 291-302.

Abstract(1659) PDF(524)

Abstract:
Here, we are discussing the applicable ranges of one-equation and two-equation turbulence models with the viewpoint of similar theory. The criterions of determining the applicable ranges of these models are given.

Extension of Poincare’s Nonlinear Oscillation Theory to Continuum Mechanics(Ⅱ)——Applications

Li Li, Huo Lin-chun

1987, 8(4): 303-316.

Abstract(2159) PDF(413)

Abstract:
This is a continuation of [1]. In [1] we suggested a method of direct perturbation of partial differential equation and weighted integration to calculate the periodic solution for continuum mechanics. In this paper, by using the above method we calculate the resonant and nonresonant periodic solutions of beam with fixed span and different boundary conditions and the resonant periodic solution of square plate under the action of concentrated periodic load. Besides, the influences of non-principal mode upon periodic solution and of static load upon amplitude-frequency curve are given.

A Free Rectangular Plate on the Two-Parameter Elastic Foundation

Sheng Yao, Huang Yi

1987, 8(4): 317-329.

Abstract(1840) PDF(678)

Abstract:
This paper provides a rigorous solution of a free rectangular plate on the V.Z. Vlazov two-parameter elastic foundation by the method of superposition^[1]. In this paper we derive basic solutions under the various boundary conditions. To superpose these basic solutions the most generally rigorous solution of a free rectangular plate on the two-parameter elastic foundation can be obtained. The solution strictly satisfies the differential equation of a plate on the two-parameter elastic model foundation, the boundary conditions of the free edges and the free corner conditions. Some numerical examples are presented The calculated results show that when the plane dimension of plate is given and the ratio between the laver depth and the plate thick is equal to 15, the two-parameter elastic model is near the Winkler's. It shows that the Winkler model can be applied to the thinner layer.

An Approach on Fixed Pansystems Theorems: Panchaos and Strange Panattractor

Zhu Xu-ding, Wu Xue-mou

1987, 8(4): 331-335.

Abstract(1843) PDF(447)

Abstract:
The investigations about chaos, at tractor and strange at tractor are main subjects in non-linear analysis. Under the framework of pansystems methodology, reference [1] discussed these problems and introduced the concepts of panchaos, panattractor and strange panattractor. These concepts omit ted the condition of continuity, compactness, etc. and put stress on the properties of binary relations on a set. A certain obtained result indicates that panchaos, panattractor and strange panattractor correspond respectively to fixed subsets of certain pansys tems operators. This paper continues the investigation of [1,2], discusses the existence of these pansystems fixed subsets, their construction and interrelations.

The Perturbation Solution of the Large Elastic Curve of Buckled Bars and the Singular Perturbation Method for Its Imperfect Bifurcation Problem

Zhou Zhe-wei

1987, 8(4): 337-345.

Abstract(1958) PDF(584)

Abstract:
This paper presents the large deflection elastic curve of buckled bars through perturbation method, and the bifurcation diagrams including the influence of the imperfection at the base by using singular perturbation method of imperfect bifurcation theory. The physical meaning of the bifurcation diagrams is discussed.

Dynamic Response of Plates on Elastic Foundations Due to the Moving Loads

Cheng Xiang-sheng

1987, 8(4): 347-356.

Abstract(1681) PDF(729)

Abstract:
This paper discusses the dynamic response of thin plates on the elastic foundations due to the moving loads by means of the varialional calculus. In the text we take the mass of moving loads into account, treat a series of questions such as the forced oscillations, the influence surfaces of the flexions and tke influence surfaces of the inner forces, resonance conditions and critical speed and so forth.

The Schrodinger Equation in Theory of Plates and Shells with Orthorhombic Anisotropy

Shen Hui-chuan

1987, 8(4): 357-365.

Abstract(1840) PDF(773)

Abstract:
This work is the continuation of the discussion of Refs. [1-5]. In this paper:[A] The Love-Kirchhoff equations of vibration problem with small deflection for orthorhombic misotropic thin shells or orthorhombic anisotropic thin plates on Winkler's base are classified as several of the same solutions of Schrödmger equation, and we can obtain the general solutions for the two above-mentioned problems by the method in Refs. [1] and [3-5].[B] The. von Kármán-Vlasov equations of large deflection problem for shallow shells with orthorhombic anisotropy(their special cases are the von Hármán equations of large deflection problem for thin plates with orthorhombic anisotropy) are classified as the solutions of AKNS equation or Dirac equation, and we can obtain the exact solutions for the two abovementioned problems by the inverse scattering method in Refs. [4-5].The general solution of small deflection problem or the exact solution of large deflection problem for the corrugated or rib-reinforced plates and shells as special cases is included in this paper.

A Theoretical Investigation on the Wave Forces on the Multiple Cylinders in Shallow Water

Su Ming-de, Pan Yu

1987, 8(4): 367-376.

Abstract(1666) PDF(601)

Abstract:
The diffraction problem of two kinds of shallow water wave, cnoidal wave and solita. wave, around a group of cylinders is discussed. A Bessel corrdinate transformation i. employed to uniform the coordinate system, and thus the boundary condition on each cylinder's surface can be satisfied by determining the coefficients in the solution. Several examples are calculated for two kinds of incident wave and various arrangement of the cylinders, and the results are discussed and compared with the available experimental data.

Generalized Derivatives of a Region Function and Its Applications

He Chong

1987, 8(4): 377-384.

Abstract(1947) PDF(632)

Abstract:
This paper is based on tome fundamental concepts in [7], Clarke's generalized derivatives[1], as well as Lasotra's and Strauss's definitions of differential D(x) of a multivalued function f(x)[6]. Thereby, the generalized derivatives of a region function f(x) is defined as D_F=∪∩{G(x)⊆B(R),∀x∈B(R);G(x)=F_x=F(x)} The existence of the generalized derivatives of a region function F(x) is discussed; the necessary and sufficient conditions of existence of the Frechet generalized derivatives of such a function is established.

1987 Vol. 8, No. 4