Longitudinal Vibration of Internally Damped Rods

Abstract

The response to sinusoidal vibration of single and coupled systems of internally damped rods has been determined theoretically. Analysis of the vibration of uniform and exponentially tapered rods has usually been simplified by the assumption that the lateral dimensions of the rods are small in comparison with the wavelength. In one example, however, the vibration of a uniform rod of significant lateral dimensions has been determined from an approximate theory given by Love, in which a lateral-inertia correction is introduced. In the Love theory, the vibration of the rod is governed by both the Young's modulus and the shear modulus of the rod material and by the damping factors that are associated with these moduli.