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中文核心期刊

1957 Vol. 1, No. 2

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ON THE PLANE POTENTIAL FLOW PAST A LATTICE OF CURVED LINE CASCADES
Tongji Lin
Methods for solving plane potential flow past a lattice of arbitrary cascades of airfoils have been given by various investigators, notably, Garrick [1], Mut-terperl [2], and [3]. As all these methods are based on. the solution of the straight line cascades, they have the drawback that the process becomes laborious for high cambered blades. To overcome this difficulty, it is suggested, in the present paper, that the part of the straight line cascades used in the above mentioned methods may be replaced by curved line cascades. To achieve this end, a simple and exact solution for plane potential flow past a lattice of curved line cascades is established. This solution contains four parameters, which can be used to adjust the inlet and the outlet angles of the blades and the solidity and the angle of the cascades.
1957, 1(2): 141-151. doi: 10.6052/0459-1879-1957-2-1957-001
1957, 1(2): 152-168. doi: 10.6052/0459-1879-1957-2-1957-002
ON TWO VARIATIONAL PRINCIPLES FOR THE NATURAL VIBRATIONS OF ELASTIC BODIES
Haichang Hu
Consider the natural vibrations of elastic bodies. For the natural frequencies, we have obtained two variational principles. In the first variational principle, an allowable state is defined as follows. The stress components and their variations have the formsand satisfy the stress-free boundary conditions. The corresponding displacement components are derived from equations of motion:Then it is proved that the natural frequencies ω of the body correspond to the extreme values of the following functional: where V is the strain energy per unit volume expressed in terms of stress components.In the second Variational principle, an allowable state is defined by any continuous stress and displacement distributions, not necessarily satisfying any equation and boundary condition. In this case, it is proved that the natural frequencies ω of the body correspond to the extreme values of the following functional:where H has the expressionPx,Py,Pz are the surface tractions, and Su is that part of
1957, 1(2): 169-183. doi: 10.6052/0459-1879-1957-2-1957-003
МАТЕМАТИЧЕСКИЙ АНАЛИЗ МАРКСИСТСКОЙ ТЕОРИИ О ВОСПРОИЗВЗДСТВЕ(Ⅱ) ОБ УСЛОВИЯХ НОДЪЕМА БЫСТРЫМ ТЕМНОм НРОИЗВОДСТВА
1957, 1(2): 184-192. doi: 10.6052/0459-1879-1957-2-1957-004
THE EFFECT OF SHEAR DEFORMATION ON THE VIBRATIONS OF ELASTIC THIN WALLED BEAMS
Haichang Hu, Wanxie Zhong
In this paper, a theory is proposed for the vibrations of elastic thin walled beams of open cross sections, where the effect of shear deformation is approximately taken into account. The theory is based on the following assumptions:1) The transverse cross section of the beam is rigid. Therefore its motion may be defined by the deflections ξ(z,t), η(z,t) and the angle of torsion θ(z,t) about the center of twist.(2) The longitudinal displacement ω(z,8,t)and the longitudiual normal stress σ(z,8,t) have the following four torms expression:3) The mean value of the shcaring stress across the thickness of beam has the following three terms expression:4) The effect of non-uniform shearing stress distribution may be counted for by introducing a twisting moment:Then the stress deformation relations, equations of motion, and boundary conditions are derived from a variational principle of reference [4], The final equations are Eqs. (24), (26), (21).In the case of beams having two planes of symmetr...
1957, 1(2): 193-204. doi: 10.6052/0459-1879-1957-2-1957-005
LARGE DEFLECTION OF A CIRCULAR CLAMPED PLATE UNDER A LINEARLY VARYING LOAD
Since Karman's equations for large deflection of a thin plate was published, some problems of symmetrical banding of circular plates have been discussed by several authors using various methods, among which the method of perturba-tion is preferable to the other methods. It is worth montioning that, in the year 1947, Prof. Chien Wei-Zang treated the problem of largo deflection of a circular clamped plate under uniform, pressure, by means of the perturbation method with the central deflection as paramelor, and that his result is in good agreement with the experimental data obrained by A-E. MePherson, W. Ramburg,and S. Levy.In this paper, the problem of large deflection of a efrcalar elaniped plate under a linearly varying load is solved, the method of perturbation with the generalized displacoment as parameter, first suggested by Mr Hu Hai Chang, being used. For the sake of convenience in application, all our results are presented, by nicely plotted curves. So far as the author knows, no
1957, 1(2): 205-232. doi: 10.6052/0459-1879-1957-2-1957-006
1957, 1(2): 233-238. doi: 10.6052/0459-1879-1957-2-1957-007