Existence of Periodic Solution for Beams With Harmonically Variable Length

Abstract

The transverse oscillatory motion of a simple beam with one end fixed while driven harmonically at the other end along its longitudinal axis is investigated. For a special case of zero value for the rigidity of beam, the problem reduces to that of a vibrating string with its corresponding equation of motion. The sufficient condition for the periodic solution of the beam was determined using the Green’s function and Schauder’s fixed point theorem. The criterion for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.