Effects of Some Structural Parameters on the Vibration of a Simply Supported Non-prismatic Double-beam System

The aim of this work is to examine the influence of some structural parameters, namely, the mass per unit length and flexural rigidity of the upper beam on the natural frequencies of a symmetric non-prismatic double-beam system elastically connected by a Pasternak-type layer. A semianalytical technique known as differential transform method was used to carry out the analysis of the vibration problem in this paper. The results of the analysis revealed that there is tendency to lower the vibration frequency of the double-beam system by increasing the mass of the upper beam. It was also found that the natural frequencies of the double-system generally increase with an increase in the flexural rigidity of the upper beam of the double-beam system. It can be concluded that both the mass per unit length and the flexural rigidity of the upper beam generally have influence on the natural frequencies of a non-prismatic double-beam system elastically coupled by a Pasternak-type elastic mediu

Vibration of an Elastically Connected Nonprismatic Double-beam System Using Differential Transform Method

In this paper, the free vibration characteristics of an elastically connected non-prismatic double-beam system based on Euler-Bernoulli beam theory are determined using differential transform method. The double-beam system is composed of two parallel non-uniform cantilever beams which are attached to each other by a Pasternak elastic medium. Numerical results of the method used are validated by comparing with the ones available in the published literature. The effect of the taper ratio on the natural frequency of the double-beam system is also studied

Variational Iteration Method for Natural Frequencies of a Cantilever Beam with Special Attention to the Higher Modes

In this work, the variational iteration method (VIM) is used to calculate the natural frequencies of a cantilever prismatic beam especially for the higher modes of vibration. The solutions yielded by VIM are validated by comparing with the natural frequencies of the said beam for lower modes earlier obtained using analytical method and the differential transform metho

Effects of internal heat generation, thermal radiation and buoyancy force on a boundary layer over a vertical plate with a convective surface boundary condition

In this paper we analyse the effects of internal heat generation, thermal radiation and buoyancy force on the laminar boundary layer about a vertical plate in a uniform stream of fluid under a convective surface boundary condition. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid whilst a stream of cold fluid flows steadily over the right surface; the heat source decays exponentially outwards from the surface of the plate. The similarity variable method was applied to the steady state governing non-linear partial differential equations, which were transformed into a set of coupled non-linear ordinary differential equations and were solved numerically by applying a shooting iteration technique together with a sixth-order Runge–Kutta integration scheme for better accuracy. The effects of the Prandtl number, the local Biot number, the internal heat generation parameter, thermal radiation and the local Grashof number on the velocity and temperature profiles are illustrated and interpreted in physical terms. A comparison with previously published results on similar special cases showed excellent agreement

Free Vibration Analysis of Tapered Rayleigh Beams resting on Variable Two-Parameter Elastic Foundation

This study aims at analyzing the effect of variable foundation parameters on the natural frequencies of a prestressed tapered Rayleigh beam having general elastically restrained ends. In this work, the elastic coefficients of the foundations are assumed varying along the beam major axis. In particular, the constant, linear and parabolic variations of the Pasternak foundation are considered. A semi-analytical approach known as differential transform method (DTM) is applied to the non-dimensional form of the governing equations of motion of the prestressed tapered Rayleigh beam and a set of recurrence algebraic equations are determined. Performing some direct algebraic operations on these derived equations and using some computer codes developed and implemented in MAPLE 18, the dimensionless natural frequencies and the associated mode shapes of the beam are obtained, the effects of these Pasternak foundation variations for various values of the slenderness ratio on the natural frequencies are investigated. It is found among others that : (i) an increase in foundation stiffness led generally to an increase in the natural frequencies; (ii) the constant elastic variations of Pasternak foundation produced highest values of natural frequencies; and (iii) the natural frequencies of tapered Rayleigh beam resting on Pasternak foundation are higher than those from the same beam on Winkler foundation. Finally, the efficiency and accuracy of differential transform method are illustrated by solving two numerical examples of vibration problems and validating the results obtained with those in the open literature, and are found to compare favorably well