应用数学和力学

1985 Vol. 6, No. 7

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Stationary-State Solutions to the Rotation of Solid Bodies with Liquid-Filled Cavities and Their Stability

Xu Shuo-chang, Dai Shi-qiang

1985, 6(7): 573-582.

Abstract(1686) PDF(560)

Abstract:
In this paper, we discuss all the possible equilibrium states of axi-symmetrical-solid bodies with liquid-filled cavities rotating around fixed axes according to the extremum conditions on the potential energy, and conclude that there exists a unique stable final-state solution, for which the system uniformly rotates around its vertical symmetrical axis, for both the inverted and suspended ones. And then applying the Lyapunov direct approach for a continuous system, we investigate the stability of the rotating systems subject to large disturbances. In addition, we describe an interesting analogue between the rotation of a solid body with a liquid-filled cavity in the inverted case and the motion of a small ball in a spinning spherical bowl. The results obtained herein theoretically provide an evidence of the reality of the secular stability.

Interlaminar Stresses of a Laminated Composite Bar under Bending (Ⅰ)

Chang Fo-van

1985, 6(7): 583-594.

Abstract(1514) PDF(600)

Abstract:
A laminated composite bar of rectangular cross section consists of a milde portion of one material and upper and lower identeal cover plates of another muterial. Uniformly distributed compressive and tensile forces each equal to p are acting respectively at the ends of the upper and lower cover plates. They form conples at both ends of the bar. Our aim is to find the interlaminar stresses or how the forces are transmitted through the glued sarfaces.

Principles of Instrumentation and Signal Processing Method of PLDA

Sun Hou-jun

1985, 6(7): 595-604.

Abstract(1912) PDF(491)

Abstract:
It is shown in this paper that in geometrical space two polarization planes of the linearly polarized light waves scattered by particles in measuring ellipsoid constitute an angle of π/2, while in sequence of lime the signals sent out by two symmetric photodetectors in PLDA are separated by a phase angle π. This property of PLDA enables the improvement of SNR.The similarity between power spectrum of pholoeleclrical current of PLDA and probability density junction P_d (u_c) of investigated flow velocity has been proved theoretically and checked by agreement of obtained results with classical theory and generally accepted experiments.

Minimal Polynomial Matrix and Linear Multivariable System (Ⅰ)

Hwang Ling, Yu Nian-cai

1985, 6(7): 605-617.

Abstract(1528) PDF(497)

Abstract:
Part (Ⅰ) of this work is on the theory of minimal polvnomial matrix and Part (Ⅱ) on the applications of this theory to linear multivariable systems.In Part (Ⅰ), concepts of annihilating polvnomial matrix and the minimal polynomial matrix of a given linear transformation in a vector group are given and the concepts of the generating system and minimal generating system of an invariant subspace for a given linear transformation are given as well. After discussing the basic properties of these concepts the relations between them and the characteristic matrix corresponding to an induced operator of a given linear transformation in any of its invariant subspace are studied in detail. The characteristics of the minimal polynomial matrix for a given vector group and the necessary and sufficient condition for the two generating systems to have the same generating suhspace is given. Using these results we can give the expression for the set of all B which makes the system x=Ax+Bu a complete controllable system for a given A.

Pinpoint Calculation of Tooth Deflection on Spur Gear by Means of the Method of Complex Variables in Plane Elasticity

Cheng Nai-shi, Liu Wen

1985, 6(7): 619-632.

Abstract(1893) PDF(685)

Abstract:
This puper incorporated and developed the method originated by A/DA. TERAUCHI. and NAGAMUYA. to which a high value is set presently at home and abroad, in which the stress and deflection of tooth on spurgears are calculated by means of the method of complex variables in plane elasticity. In this paper, their approximate solution was developed to become exact solution. The accuracy of the mapping shape of tooth was increased. It was mentioned that the mapping junction was expressed by five fractional terms, with the mapping error being less than 1% m. A calculating principle was proposed to find out the displacement of contact point in relation to central line of the ndiacent gear tooth affecting the quality of mesh of gears directly. The computer program was made, and according to the computed results, the figures were given so that the displacement of the contact point in the normal direction can be calculated conveniemly for engineering calculation.

A New Method for Calculating the Fundamental Potential Functions Induced by a Source/Dipole Polygon

Fang Zhong-sheng

1985, 6(7): 633-638.

Abstract(1613) PDF(531)

Abstract:
In dealing with calculation of the normal potential velocity induced by a source polygon there Has a known result derived by Hess and Smith[1] in terms of local coordinates of the polygon's corners and the point to be considered under a coordinate axis system located in the polygon. The present method in terms of their global coordinates is an alternative and extension to it. Hence, there is no need to transform coordinates of points and integrate ∫∫(1/r)dS, etc. numerically in the calculation.

The Generalized Variational Principes with their Applications in Structural Analysis

Cheng Xian-sheng

1985, 6(7): 639-640.

Abstract(1645) PDF(538)

Abstract:
This paper will chseuss the generalized variational prinetples.which the established bythe methed of undetermined multipliers in structures.and analys the statiedllyindeterminate truss.in which these principles will be used.At the same time we bring asymmetrical matrix and give speeitie sohution.thus all the internal forees of structures maybe found.

Geotechnical Yield Criteria and Constitutive Relations in Strain Space

Chen Chang-an, Zheng Ying-ren

1985, 6(7): 648-654.

Abstract(1824) PDF(630)

Abstract:
Based on Ilyushin's postulate, this paper deals with the necessity and features of researching the geotechnical elasto-plastic theory in strain space. In the paper, we established the relations between stress in variants and elastic strain invariants, brought about the transformation from the stress yield surfaces into the strain yield surfaces, derived and discussed the strain expressions from 12 yield criteria expressed by stress. By normality rule, we also derived 12 constitutive relations for ideal plastic materials associated with the above expressions. The results presented here can be applied to practice and are helpful to the study of the plastic theory in strain space.

A New Approximate Solution of Nonlinear Diffusion Equation

Yuan Yi-wu

1985, 6(7): 655-659.

Abstract(1390) PDF(612)

Abstract:
In this paper, the same problem in ref. [1] is studied. The author's solution approximately satisfies the whole fundamental equations (1,1) and (1.2), and the whole bound values conditions (1.3-1.5). But the Liu's solution(1) does not satisfy the equation of continuity (1.2).

A Kind of Nonlinear Oscillations of Single Degree of Non-Autonomy System

Wang Xin-zhi, Zhu Tong-xin

1985, 6(7): 661-669.

Abstract(1708) PDF(561)

Abstract:
In this paper we use the method of derivative expansion of multiple scales of singular perturbations, and we have solve the forced vibration equation of a particle attached to a nonlinear spring under the influence of slight viscous damping. The problem is of the fourth order nonlinearity. The four cases discussed are the soft excitation of non-resonance, the hard excitation of non-resonance, the soft excitation of resonance, the hard excitation of resonance.