Free Vibration Analysis of Timoshenko Sandwich Beam Tapered Along Thickness and Width Resting on Pasternak Foundation

Abstract

This study delves into the analysis of the free vibration characteristics of a Timoshenko sandwich beam tapered along both width and thickness, subjected to an axially pulsing load on a Pasternak foundation. Integral to this investigation are the comprehensive considerations of energy expressions encompassing bending, axial deformation, kinetic energy, and strain energy induced by transverse shear stress. Subsequently, the differential equations governing the system, along with the associated boundary conditions, are deduced utilizing Hamilton's principle, followed by their non-dimensionalization. Leveraging series solutions from prior research that satisfy these equations and boundary conditions, each coordinate of the system is addressed. In the quest for a deeper understanding, Galerkin’s energy principle is employed to derive matrix expressions for key parameters such as mass and stiffness. Utilizing these matrices, Eigenvalues are computed to ascertain the natural frequencies of the system. The findings are presented through a series of graphical representations, elucidating the influence of various system parameters.