Dynamic Behavior of Bernoulli-Euler Beam with Elastically Supported Boundary Conditions under Moving Distributed Masses and Resting on Constant Foundation
Adeoye Adebola Samuel
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
Akintomide Adeniyi *
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria
*Author to whom correspondence should be addressed.
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.
Keywords: Bi-parametric foundation, shear deformation, resonance, critical speed, natural frequency, beam, modified frequency