On The Free Vibration Analysis of Simply Supported Beam with Shear Deformation

Abstract

This paper considered the free vibration analysis of a simply supported beam with shear deformation. The governing equation of fourth order partial differential equation was reduced to an ordinary differential equation using series solution which is the solution of the governing equation. Numerical result was presented and plotted against x, it was found that the response amplitude of the beam increases with increase in the length of the beam and radius of gyration but reduces with an increase in foundation modulus and shear modulus. To keep the deflection of the beam in check, there’s need to keep the length of the beam and the radius of gyration in check to avoid over deflection of the beam which can cause damage in building structures and so on.