1985 Vol. 6, No. 10

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The Method of Continuous Distribution of Singularities to Treat the Stokes Flow of the Arbitrary Oblate Axisymmetrical Body
Zhu Min, Wu Wang-yi
1985, 6(10): 859-871.
Abstract(2102) PDF(795)
Abstract:
This paper deals with the Stokes flow of the arbitrary oblate axisymmetrical body by means of constant density and quadratic distribution function approximation for the method of continuous distribution of singularities. The Sampson spherical infinite series arc chosen as fundamental singularities. The convergence, accuracy and range of application of both two approximations are examined by the unbounded Stokes flow past the oblate spheroid. It is demonstrated that the drag factor and pressure distribution both conform with the exact solution very well. Besides, the properties, accuracy and the range of application are getting belter with the improving of the approximation of the distribution function. As an example of the arbitrary oblate axisymmetrical bodies, the Stokes flow of the oblate Cassini oval are calculated by these two methods and the results are convergent and consistent. Finally, with the quadratic distribution approximation the red blood cell, which has physiologic meaning, is considered and for the first time the(orresponding drag factor and pressure distribution on the surface of the cell are obtained.
Vibration Theory of Continuous Beam under the Action of Moving Load
Yeh Kai-Yuan, Ma Guo-lin
1985, 6(10): 873-878.
Abstract(2288) PDF(690)
Abstract:
This paper uses the small parameter method to investigate the dynamic calculation of the whole vibration process of trains passing through a continuous beam, considering the effects of the mass and the damping as well as the masses of the moving loads. By solving a set of integral equation, we find out the general solution of continuous beam under the action of arbitrary moving load PF(t) and calculate the case of single moving load being Q#em/em#+P#em/em#sin(a#em/em#t + b#em/em#). By concluding our results, we establish the dynamic theory of vibration of continuous beam acted by the moving load.Finally, as an example, we calculate the vibration question of two-span continuous beam. The deflections of two midspan are shown in Fig. 2 and Fig. 3.
Integral Invariant in Noncoservative Systems and Its Application in Modern Physics
Liu Cheng-qun, Luo Shi-yu
1985, 6(10): 879-885.
Abstract(2268) PDF(604)
Abstract:
In this paper, the Poincaré and Poincaré-Cartan integral invariants in nonconservative systems are established. According to the integral invariant, he non-linear oscillation of particles in 3-folded symmetry spiral sector cyclotron is investigated, It turns out that the method is successful.
The Schrodinger Equation of Thin Shell Theories
Shen Hui-chuan
1985, 6(10): 887-900.
Abstract(2309) PDF(1351)
Abstract:
This work is the continuation of the discussions of [50] and [51]. In this paper:(A) The Love-Kirchhoff equation of small deflection problem for elastic thin shell with constant curvature are classified as the same several solutions of Schrödinger equation, and we show clearly that its form in axisymmetric problem;(B) For example for the small deflection problem, we extract me general solution of the vibration problem of thin spherical shell with equal thickness by the force in central surface and axisymmetric external field, that this is distinct from ref. [50] in variable. Today the variable is a space-place, and is not time;(C) The von Kármán-Vlasov equation of large deflection problem for shallow shell are classified as the solutions of AKNS equations and in it the one-dimensional problem is classified as the solution of simple Schrödinger equation for eigenvalues problem, and we transform the large deflection of shallow shell from nonlinear problem into soluble linear problem.
The Three-Dimensional Unsteady Boundary Layer over an Impulsively Started Rotating Disk
Chen Y. M
1985, 6(10): 901-904.
Abstract(2027) PDF(755)
Abstract:
The unsteady boundary layer over an impulsively started rotating disk is studied, a complete solution describing the smooth transition from vortex diffusion at ωt=0 to Kármán's steady solution is obtained by series expansion and its numerical continuation. The angle of body streamlines, together with experimental values, are given as the function of time t as well as the moment coefficient CM and on-coming velocity ω(∞).
Minimal Polynomial Matrix and Linear Multivariable System(Ⅱ)
Hwang Ling, Yu Nian-cai
1985, 6(10): 905-922.
Abstract(2259) PDF(597)
Abstract:
Part(Ⅰ) of this work is on the theory of minimal polynomial matrix and Part(Ⅱ) is on the applications of this theory to linear multivariable systems.In I of this part, using the theory in Part(Ⅰ), some results about input part of a linear multivariable system are discussed in detail and in Ⅱ, using duality properties, the concepts about row n.p.m.and row generating system, etc. are given, and some results about output part of linear multivariable system are discussed, too. In Ⅲ, we discuss the approach which can give the polynomial model with less dimension from the state-space modeland in Ⅳ we discuss tha inverse of the problem to give the state-space model from the polynomial model. Some interesting examples are given to explain the theory and the approach.
Pansymmetry and Fixed Pansystems Theorems of a Class of Pansystems Relations
Wu chen
1985, 6(10): 923-928.
Abstract(2024) PDF(592)
Abstract:
In this paper, some results of pansymmetry and fixed pansy stems theorems are extended to the case of a class of binary relations under the framework of pansystems methodology. It is concretely discussed when a class of binary relations has a common fixedsubset on a finite universal set. Several simple but comprehensive decisive theorems are obtained which can be determined if a class of binary relations has a common fixed subset. As a result. the mum decisive theorem——Markov-Kakutani Theorem——is extended, which is in traditionally fixed point theory and can be determined if a class of mappings has a common fixed point.
Harmonic Solutions of Some Second-Order Nonlinear Equations under a Periodic Force
Ge Wei-gao
1985, 6(10): 929-937.
Abstract(2080) PDF(556)
Abstract:
In this paper we prove some theorems on the existence of harmonic solutions of some second-order nonlinear equations under a periodic force. These theorems extend relevant results in refs [1]-[8].
Elastic Perfectly-Plastic Fields at a Rapidly Propagating Crack-Tip
Lin Bai-song
1985, 6(10): 939-946.
Abstract(2227) PDF(672)
Abstract:
All the stress components at a rapidly propagating crack-tipin an elastic perfectly-plastic material are the functions of θ only. Making use of this condition and the equations of steady-state motion, stress-strain relations and yield conditions, we obtain the general solutions in both the cases of anti-plane and in-plane strain. Applying these two general solutions to propagating Mode Ⅲ and Mode I cracks, respectively, the elastic perfectly-plastic and the perfectly-plastic fields at the rapidly propagating tips of Mode Ⅱ and Mode I cracks are derived.
Calculation of Orthotropic Shallow Conoidal Shell Roofs
Cheng Xiang-sheng
1985, 6(10): 947-952.
Abstract(2042) PDF(496)
Abstract:
The present paper is to introduce the method for the calculation of the roof with orthotropic shallow conoidal shells which are always used in the industrial buildings. Since the middle surface of the shallow conoidal shell having the variable curvatures and twists, therefore the system of fundamental equations, which are obtained by us, are being possessed of the variable coefficients.If we want to find the exact analytical solutions, it will be involved in great mathematical difficulties. This paper gives the approximate solutions of the orthotropic shallow conoidal shell roof which is simply supported at all edges and under the uniformly distributed load. In this paper the method of small parameter is used.
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