Influence of Rotatory Inertial Correction Factor on the Vibration of Elastically Supported Non-Uniform Rayleigh Beam on Variable Foundation

Abstract

The influence of rotatory inertial correction factor on the vibration of elastically supported non uniform Rayleigh beam under moving distributed masses and resting on variable bi-parametric elastic foundation is investigated. The governing equation is a fourth order partial differential equation with variable and singular co-efficients. In order to solve this equation, the method of Galerkin is used to reduce the governing differential equation to a sequence of coupled second order ordinary differential equation which is then simplified with modified asymptotic method of Struble. The simplified equation is solved using the integral transformation technique. The analysis of the closed form solution shows that resonance is attained earlier in moving mass system than in the moving force system. The results in plotted graphs show that as the rotatory inertia, foundation modulus and shear modulus increase, the deflection of the elastically supported non-uniform Rayleigh beam decreases in each case. The transverse deflections of the elastically supported beam on variable bi parametric elastic foundation are higher under the action of moving masses than those when only the force effects of the moving load are considered. This implies that resonance is reached faster in moving mass problem than in moving force problem.