Free Vibration Behavior of Prestressed Beams

Abstract

A Rayleigh-Ritz free vibration analysis of a simply supported beam is carried out in this note with prestress effects included through an axial compressive load and with shear deformation and rotatory inertia considered. Suitable functional forms are assumed for the lateral displacement and the shear rotation. Results in the form of frequency parameters for various modes are presented. The variation of the frequency parameters with slenderness ratio (length/radius of gyration) and the magnitude of the compressive load (prescribed as different percentages of the critical load of the beam) is clearly brought out through numerical results. It is observed that the effect of shear deformation and rotatory inertia is quite significant for higher modes of vibration of slender beams and the effect of axial compressive load is predominant for lower modes of vibration.