Analytical Polynomial Solutions for Vibrating Axially Graded Beams

Abstract

ABSTRACT Vibration and buckling of simply supported axially graded beams, that is, those with inertial coefficient and stiffness, which vary with axial position are discussed. New closed-form solutions are derived for the natural frequency of the beam. The semi-inverse problem of finding the distributions of the stiffness and the inertial term so that the preselected polynomial functions serve as an exact mode shape of the inhomogeneous beam is solved.