Title Problem Research Articles

Forced vibrations of a continuous beam with ends elastically restrained against rotation

A survey of the literature shows that the title problem has not been studied to any great extent. In the present paper an approximate solution is obtained in the case of a beam with ends elastically restrained against rotation and an intermediate support. A sinusoidally varying excitation is assumed.

Fundamental frequency of composite circular membranes with boundary disturbances

Abstract The title problem constitutes a basic mathematical model where the separate or combined effects of possible manufacturing flaws are taken into account. These flaws are (a) deviations with respect to the ideal circular shape and (b) presence of a central inhomogeneity. The effects of these complicating factors on the fundamental frequency of a membrane are calculated using two approximate analytical techniques and the finite element method. Excellent agreement is shown to exist between the results obtained by the three different approaches.

Effect of a concentrated mass on large amplitude, free flexural vibrations of elastic plates and beams

This paper presents an approximate solution to the title problem for the following situations: (a) supported and clamped rectangular plates, (b) circular plates with edges elastically restrained against rotation, and (c) beams with ends flexibly attached. The approach is quite simple and it is shown that the engineering accuracy achieved is satisfactory from the point of view of the determination of fundamental frequencies in a wide variety of structural elements commonly used in transducer design and aerospace and naval engineering applications.

Vibrations of corner point supported shallow shells of rectangular planform

AbstractThe first known solution of the title problem is presented. The Ritz method is used, with algebraic polynomials forming the set of trial functions. The condition that all three components of displacement be zero at the four corners is straightforwardly enforced. Numerical studies show that the convergence is relatively slow, requiring more terms than for shells which are completely free. The class of problems studied includes independent, constant curvature in each of the directions parallel to the edges, yielding vibration modes which fall into one of four symmetry classes, with symmetry or antisymmetry of the displacements existing with respect to each of the two symmetry axes of the problem. Detailed results are given for the frequencies and mode shapes of the first two modes of each symmetry class for shells having square planform and circular cylindrical, spherical and hyperbolic paraboloidal curvatures. Accuracy of the results is partially established by comparison with other previously published, accurate results for the corner supported flat square plate.

Internal and Edge Cracks in a Plate of Finite Width Under Bending

In this paper the title problem is studied by using Reissner’s transverse shear theory. The main purpose of the paper is to investigate the effect of stress-free boundaries on the stress intensity factors in plates under bending. Among the results found particularly interesting are those relating to the limiting cases of the crack geometries. The numerical results are given for a single internal crack, two collinear cracks, and two edge cracks. Also studied is the effect of Poisson’s ratio on the stress intensity factors.

Transverse vibrations of a beam elastically restrained at one end and with a mass and spring at the other subjected to an axial force

This paper deals with the exact solution of the title problem. The classical theory of vibrations of beams is used and a tabulation of eigenvalues is presented as a function of some of the governing mechanical parameters. The problem is of basic interest in several areas of engineering, specially to nuclear reactor systems designers since in many instances pumps or other electromechanical arrangements are placed at the end of a clamped beam.

Effects of Damping and Circulatory Forces on Dynamic Instability of Gyroscopic Conservative Continuous Systems

ABSTRACT ABSTRACT The title problem is studied, with emphasis on the small damping and circulatory force case. It is shown that small internal and/or external damping forces and/or smalt (as well as large) circulatory forces in general destabilize an otherwise stable gyroscopic conservative system. A condition for no destabilizing effects of these small forces is obtained, A concept of perfect system in elastic stability of nonconservative problems is also presented. An example problem is given for demonstration purposes.

Antisymmetric vibrations of circular plates with thickness varying in a bilinear fashion

The title problem is tackled using simple polynomial co-ordinate functions and the Ritz method. The algorithmic procedure is quite straightforward and yields very accurate results in the case of circular plates of uniform thickness. It can also be easily implemented by a desk computer.

Pulsatile pipe flow pseudoplastic materials; The flow enhancement for Re ≪ 1

Solution of the title problem for the power-law model of viscosity function is constructed by the method of small parameter in the region of small Reynolds numbers. The main result of the paper is a quantitative estimation of the values of Re, when the influence of inertia on flow enhancement may be quite neglected.

A note on transverse vibrations of continuous beams subject to an axial force and carrying concentrated masses

Polynomial co-ordinate functions are used in order to obtain an approximate solution to the title problem. The algorithmic procedure is quite simple, leads to adequate engineering accuracy and can be easily extended to the case of several intermediate supports.

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface—II. Solution and results

The analysis of the title problem was given in Part I. In this part the numerical method for solving the problem is described and the stress intensity factors obtained from the solution for various crack geometries are presented.

Electrochemical dehalogenation of open-chain vicinal dihalides at mercury cathodes: The effect of leaving group identity on E1/2 values and on steric course

The title problem has been investigated polarographically in the homologous series of erythro and threo-5,6-dihalodecanes (X = Br, Y = I; X == Cl, Y = I; X = F, Y = I; X = Br, Y = Br; X = Cl, Y = Br; X = F, Y = Br; X = Cl, Y = Cl; X = F, Y = Cl). Each dihalide from the series gave a single two-electron wave. A very pronounced dependence of half-wave potential on halogen group identity was found in the series, the E1/2 values ranging from -0.3 V (X = Br, Y = I) to -2.8 V (X = F, Y = Cl). Controlled-potential electrolyses of the dihalides were accomplished at mercury pool electrode affording always cis- and/or trans-5-decene as the sole product, in almost quantitative (>90%) yields. Stereochemistry of the dehalogenation was deduced from the olefin-isomer distribution data determined by VPC. Very marked differences were found in the series, the elimination stereochemistry ranging between a clean anti and a prevalent syn, in dependence on the identity and configuration of the halogen groups.

Vibration and buckling of circular plates of variable thickness

The Ritz method and polynomial coordinate functions are used to obtain an approximate yet quite accurate and simple solution to the title problem. Results of frequency and buckling coefficients are obtained as a function of several combinations of the governing mechanical parameters.

Vibrations of a beam elastically restrained against rotation at one end and carrying a guided mass at the other

An exact solution to the title problem is obtained in the present paper using classical beam theory. Natural frequencies and mode shapes are determined as a function of the end flexibility coefficient and of the ratio concerned, end mass/beam mass.

Transverse vibrations of rectangular orthotropic plates with the edges elastically restrained against rotation and a free, straight corner cut-out

A survey of the literature reveals that the title problem has not been previously solved. Frequent applications of composite materials in many fields of modern technology—from ocean and aerospace engineering to printed circuit boards—have generated the need for a sound understanding of the dynamic behaviour of orthotropic and isotropic plates. The fundamental frequency of transverse vibration of the orthotropic structural element is determined by expanding the displacement amplitude function in terms of simply polynomial coordinate functions which satisfy identically the essential boundary conditions and approximately the natural requirements. The Ritz method is used to generate the frequency equation.

Anomaly observed in the approximate analysis of vibrating rectangular plates with edges elastically restrained against rotation and translation

This paper deals with the solution of the title problem in the case of an orthotropic plate with three edges elastically restrained against rotation whilst transverse displacement is prevented. It is assumed that the fourth edge is elastically restrained against rotation and translation. The natural boundary conditions are satisfied approximately at the fourth edge. The Rayleigh-Ritz method is used to derive an approximate fundamental frequency equation and a rather curious anomaly is shown to exist in the frequency values for a certain range of values of the rotational and translational spring parameters which govern the motion of the fourth edge.

The additional settlement of a rigid circular foundation on an isotropic elastic halfspace due to multiple distributed external loads

The paper is concerned with the interaction between a rigid circular foundation resting on an elastic halfspace and a distributed external load of finite extent which acts at an exterior region of the halfspace. This problem serves as a model for the examination of the interaction between an existing structural foundation and a newly constructed adjacent foundation. The mathematical procedures which lead to the theoretical analysis of the title problem are summarized. It is shown that the additional elastic settlements experienced by the rigid circular foundation due to the action of a concentrated external force can be evaluated in exact closed form. This solution is used to generate results which are applicable to distributed loadings. From the results presented it is possible to determine the additional elastic settlement of a rigid circular foundation on an elastic halfspace due to multiple loads, of arbitrary shape and location, which act in its vicinity. La communication traite de l'interaction entre une foundation rigide circulaire reposant sur un semi-espace et une charge extérieure répartie de surface finie qui agit sur une zone extérieure à la surface du semi-espace. Ce problème sert de modéle à l'étude de l'interaction d'une fondation structurale existante et d'une fondation contiguë nouvellement construite. Les procédés mathématiques qui ont conduit à l'analyse théorique du problème énoncé en titre sont résumés et il est montré que les tassements élastiques supplémentaires subis par la fondation rigide circulaire, dus à l'action d'une force externe concentrée, peuvent, se calculer d'une manière exacte. Cette solution sert pour obtenir des résultats qui sont applicables à des charges réparties. A partir des données énoncées, il est possible de déterminer le tassement élastique supplémentaire que subira une fondation circulaire rigide sur un semi-espace élastique sous des charges multiples de forme et de localisation arbitraires, intervenant dans son voisinage.

Vibrations of a clamped rectangular plate of generalized orthotropy with a free, straight corner cutout

An exact solution of the title problem is probably out of the question. It is shown in the present study that a very simple solution can be obtained using simple polynomials and the Ritz method. The displacement amplitude is approximated in terms of a polynomial which identically satisfies the prescribed boundary conditions along the orthogonal edges but not along the corner cutout.

Fundamental frequency of orthotropic plates subject to in-plane shear forces

A general yet quite simple approach is proposed to deal with the title problem. It is assumed that the plate edges are elastically restrained against rotation. Numerical results are presented for orthotropic configurations as well as for some isotropic cases not previously considered by other investigators.

強風下の双錨泊船の振れ回りと錨鎖張力に関する模型実験

In order to find a weak point for mooring, authors carried out the model experiments on the above title problem by using of 1/50 scale model of GT 5,000 ton cargo ship. The external force acting on the model ship in a water tank with generator is wind force, no wave. The wind-direction were changed at every 15 degrees from the line drawed vertically to a line between both anchors. Main experimental results are as follows; (1) A Open-moor of which the leg angle between both chain cables is about 60° is more safety because of smaller yawing motion, as that being obtained by YONEDA. However, it should be taken notice that the shock load acting on the riding cable is greater than that at a single anchor, if the wind-direction is agreed with each cable line, and also that the most possibly raises a dragging anchor in such case. (2) Using Engine-astern in order to control the yawing motion at anchor has the effect of checking gently and smaller, as that being obtained by T.S.HOKUTO-Maru. However, such engine motion at anchor under heavy weather will be brought on the dragging anchor owing to the shortage of an anchor-holding power.