Dynamic Behavior of Bernoulli-Euler Beam with Elastically Supported Boundary Conditions under Moving Distributed Masses and Resting on Constant Foundation
Journal Title: Asian Research Journal of Mathematics - Year 2017, Vol 4, Issue 4
Abstract
The dynamic behavior of uniform Bernoulli-Euler beam with elastically supported boundary conditions under moving distributed masses and resting on constant foundation is investigated in this research work. The governing equation is a fourth order partial differential equation with variable and singular co-efficients. In order to solve this equation, the method of Galerkin is used to reduce the governing differential equation to a sequence of coupled second order ordinary differential equation which is then simplified by applying the modified asymptotic method of Struble. The simplified equation is solved using the Laplace transform technique. The analysis of the closed form solution in this research work shows the conditions for resonance as well as the effects of beam parameters for moving force system only. The results in plotted graphs show that as the axial force, foundation modulus and shear modulus increase, the transverse deflection of the uniform Bernoulli-Euler beam with elastically supported boundary conditions decreases.
Authors and Affiliations
Adeoye Adebola Samuel, Akintomide Adeniyi
Keywords
Related Articles
- EP ID EP338485
- DOI 10.9734/ARJOM/2017/33156
- Views 69
- Downloads 0
On Varanovskaya Type Theorem for Generalized Bernstein-Chlodowsky Polynomials
In this paper we proved Varanovskaya type theorem for generalized Bernstein-Chlodowsky polynomials.
Numerical Study of the Effects of Suction and Pressure Gradient on an Unsteady MHD Fluid Flow between Two Parallel Plates in a Non-Darcy Porous Medium
The present problem discusses the unsteady MHD fluid flow of viscous incompressible fluid in between two parallel horizontal plates, upper being at rest and lower moving, in the presence of transverse magnetic field in a...
A Computation of the Casimir Energy on a Parallelepiped
The original computations deriving the Casimir energy and force consists of first taking limits of the spectral zeta function and afterwards analytically extending the result. This process of computation presents a weakn...
Computational Method for the Determination of Forced Motions in Mass-spring Systems
In this paper, we propose a computational method for the determination of forced motions in mass-spring systems. The method of interpolation and collocation of Hermite polynomial (as basis function) was adopted to genera...
Problem Solving Framework for Mathematics Discipline
This paper identifies a 4-step framework that can be implemented in almost every mathematics lesson and training setting to move learners towards problem solving effectively. This framework which is built upon existing i...