关于一个圆轴的粘弹性扭转问题

不用粘弹性力学中的相应原理,直接求解文［１］提出的一个圆轴的粘弹性扭转问题,这种解法比文［１］的方法要简便得多．     

Natural frequencies of circular arcs with varying cross section

This paper presents a transter matrix method for conveniently predicting the natural frequencies of circular arcs with varying cross section. The equations of in-plane vibration of an arc are written as a coupled set of first-order differential equations by using the transfer matrix of the arc. Once the transfer matrix has been determined, the natural frequencies and the mode shapes of the vibration are calculated in terms of the elements of the matrix for a given set of boundary conditions at the ends of the arc. The numerical results obtained by the method are compared with the experimental results for free-clamped arcs with tapered breadth, which are in good agreement with each other.     

On the repeated natural frequencies for torsional vibration of shafts

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Stress bounds for twisted bars of strip cross section

Bounds are established for the maximum resultant shear stress, and used to investigate the approximation involved in the value predicted for thin sections on the basis of the membrane analogy.     

Magnetohydrodynamic pipe flow in ducts with partial circular ring cross section and annular cross section

In this paper we use the Green function method to solve the problem of steady one dimensional flow of an incompressible viscous, electrically conducting fluid through a pipe with partial circular ring cross section and one with annular cross section, in the presence of an applied transverse uniform magnetic field. We obtain analytic solutions and carry out some numerical calculations of the velocity distribution and induced magnetic field.     

On the dynamic behaviour of rotating shafts under combined axial and torsional loads

Meccanica - A comprehensive dynamic study on a distributed parameter model of a straight uniform rotating shaft is developed, aimed at presenting some clarifications and corrections to published...     

An analytical model for plug flow in microcapillaries with circular cross section

Plug flow in microcapillaries or microchannels offers significant advantages for the development of microfluidic applications and recently triggers many interests and studies. Recirculation is formed within liquid plugs due to the presence of interfaces. This paper presents an analytical model to investigate the recirculation flow and the flow resistance in microcapillaries with circular cross section. A fourth order partial differential equation is used to model the Stokes flow within the liquid plug. The results of the flow field show that the flow pattern is affected by the plug length. The flow resistance is determined through the force balance of the liquid plug. The comparison of the flow field and the flow resistance from the analytical model and the experiments shows good agreement.     

Propagation of elastic waves in circular rods homogeneous over the cross section

Propagation of elastic waves in circular rods and in rods with a cylindrical cavity is numerically studied. The influence of the rod size on the wave propagation velocity is analyzed. A phenomenon of repeated rebound in short homogeneous rods is described.     

变截面梁柱刚度方程的Bessel函数解

本文提出了一个计算Bessel函数Jp(x)及Np(x)的近似方法并在－∞＜P＜∞和X＞0的范围内验证了方法的适用性,进而提出了截面按幂涵数变化的变截面梁柱的刚度方程并研究了其临床其临界力。∞     

Acoustic waves in a cylindrical duct with periodically varying cross section

The null field approach is used to study the propagation of acoustic waves in a rotationally symmetric hard-walled duct with a periodically varying cross section. For a radius that varies sinusoidally along the axial distance, numerical computations give the axial wave number and the passbands and stopbands of the modes of the duct. In particular, small passbands are seen to exist even for very large variations in radius, and probably all the way to the point where the duct is cut off. We also present some plots which show the pressure pattern inside the duct.     

Laminar velocity profile development in straight pipes of circular cross section

Velocity profile development has been studied experimentally in Newtonian and some non-Newtonian fluids. The entry length for the development of 99% of the terminal axial velocity from an initially flat profile has been found to be given byZ _e = 1.1–0.112N(Re) for laminar flow Reynolds numbers between 1 and 1500 with Newtonian fluids. There were substantial increases in this length for weakly visco-elastic aqueous solutions of polyethylene oxide and polyacrylamide in the Reynolds number range (between 1 and 10) where these have been studied.     

On the choice of the reference frame for beam section stiffness properties

This work discusses the choice of a reference frame for beam section stiffness properties. Established concepts as the center of elasticity, the center of stiffness and the center of compliance are discussed and contextualized. An interpretation of univocally defined generalized strain transformations is given in terms of minimization of appropriate norms of the stiffness and compliance matrices of the beam section that univocally define special reference points. Transformations of generalized strain perturbations that preserve the angular strain are sought. They are subsequently constrained to represent a change of reference point, and further restricted to lie in the plane of the section. Each transformation is univocally defined and given a clear mathematical and geometrical interpretation. It is recognized that transformations that decouple forces and linear strains from moments and angular strains cannot be described as a mere change of reference point.     

On the rotating rod with variable cross section

Summary Stability of a heavy rotating rod with a variable cross section is studied by energy method. Bifurcation points for the system of equilibrium equations are analyzed. It is shown that for the case when the rotation speed exceeds the critical one, the trivial solution ceases to be the minimizer of the potential energy, so that rod loses stability, according to the energy criteria. Also, a new estimate of the maximal rod deflection in the post-critical state is obtained. Accepted for publication 11 November 1996     

Direct numerical modeling of three-dimensional turbulent flows in pipes of circular cross section

Turbulent viscous incompressible flows in pipes of circular cross section are subjected to a detailed numerical investigation on the Reynolds number interval from 2000 to 10 000. The evolution of the motion and the distribution of the average characteristics in the limiting regimes are studied. A detailed comparison shows good general agreement between the results of the calculations and the known experimental data. Possible causes of the differences are discussed.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 14–26, November–December, 1994.     

Arc Hyperbolic sine creep theory applied to torsion-tension member of circular cross section

A multiaxial creep theory is presented in this paper which will predict the total deformations of a load-carrying member at any specified time after load. Load-deformation relations are derived based on the assumption that the isochronous stress-strain diagram of the material can be represented by an arc hyperbolic sine function [see, eq (2)]. A closed solution was obtained for the torsion-tension member considered in this investigation. Experimental data were obtainsed for nylon and high-density polyethylene members in a controlled-environment room and for 17-7PH stainless-steel members at 972° F. Good agreement was found between theory and experiment.Formerly with Department of Theoretical and Applied Mechaaics, University of Illinois, Urbana, Ill.Paper was presented at 1963 SESA Spring Meeting held in Seatle, Wash., on May 8–10.