Closed-Form Solution for Free Longitudinal Vibration of a Bar with Rayleigh and Love Correction Term

Abstract In this paper, the previous solutions obtained for the natural frequency of classical inhomogeneous bars are extended to include the correction terms by Rayleigh and Love. The solution is derived by a semi-inverse method, consisting of the postulation of mode shape and tailoring elastic modulus and Poisson's ratio so that the mode shape satisfies the boundary conditions and the governing differential equation.