EXISTENCE OF PERIODIC-SOLUTION FOR BEAMS WITH HARMONICALLY VARIABLE-LENGTH

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 corr esponding equation of motion. The sufficient condition for the periodi c solution of the beam was determined using the Green's function and S chauder'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.