Dynamic Response of Axial Forced Rayleigh Non-uniform Beam Under Accelerating Distributed Load

Abstract

This research examines the dynamic response of axial forced Rayleigh non-uniform beam under accelerating distributed load. The governing partial differential equation of order four and the transverse deflection in which the simply supported Rayleigh beam of finite length under accelerating distributed load was considered. The effects of axial force values, shear modulus, foundation modulus, load speed and gyrating radius in connection with the length of the span of a Rayleigh beam were investigated. The fourth order partial differential equation in equation was reduced to a second order differential equation using the Fourier sine finite integral transformation method. Starting with the definition of the Fourier sine finite for, the simplified second order differential equation is solved using the Laplace transform. Numerical results were presented and it was observed that for all values of various axial force, the deflection is constant from the origin, but there is a minor difference on the positive side. Also, the result showed that for all values of shear modulus, the deflection remains constant. It was further observed that the midpoint deflection of the Rayleigh beam increases as load speeds, foundation modulus and gyrating radius increases. Finally, the results obtained are validated and are found to compare favorable well with those in the open literature.

Keywords

• Rayleigh beam; Laplace transform; foundation modulus; axial force; shear modulus