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ABSTRACT

Background: The dynamic analysis of beams resting on elastic foundation is one of the important topics in engineering and applied Mathematics and is a subject of investigation for many decades. Objectives: The specific aim of this paper is to find the analytical solutions to the governing fourth order partial differential equation that involves the variable elastic subgrade and variable magnitude distributed load on the system. Methods: Use is made of the elegant method of Galerkin and convolution theory. Results: From the analytical and numerical solutions, as the variable elastic foundation, damping, and axial force increases, the response amplitudes of thin beam under the action of harmonic varying distributed loads with constant velocity decreases and are displayed in the form of plots. Conclusions: The analytical solutions to the governing fourth order partial differential equation for thin beam is solved and the dynamic effects of some vital parameters are discussed.
Keywords: Harmonic loads, Variable subgrade, Thin beam, Simply supported, Axial force.