ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Transverse Response of a Structural Member with Time Dependent Boundary Conditions to Moving Distributed Mass

Journal of Environmental Accounting and Management 8(2) (2019) 167--187 | DOI:10.5890/JAND.2019.06.002

Babatope Omolofe$^{1}$, Alimi Adedowole$^{2}$

$^{1}$ Department of Mathematical Sciences, School of Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria

$^{2}$ Department of Mathematical Sciences, Faculty of Sciences, Adekunle Ajasin University, Akungba-Akoko, Ondo State, Nigeria

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Abstract

This paper investigates the dynamic response of a simply-supported uniform beam resting on elastic subgrade and subjected to travelling distributed load. A robust mathematical procedure is developed to treat this vibrating system problem. In particular, the Mindlin and Goodman’s technique in the first instance is used to transform the non-homogeneous fourth order partial differential equations with governing non-homogeneous boundary conditions into non-homogeneous fourth order partial differential equations with homogeneous boundary conditions and then the resulting transformed equation is then further treated using the versatile generalized integral transform with the series representation of the Heaviside function and a modification of Struble’s asymptotic method. Analytical solution was obtained for the dynamic response of the uniform elastic beam. Analytical and Numerical calculations give important results which is very useful in structural design and engineering analysis.

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