Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement— Part I: Theory

Theoretical analyses are presented for nonlinear vibrations of a clamped rectangular plate under a uniformly distributed periodic load, with the effect of both initial deflection and initial edge displacement taken into consideration. The dynamic analog of the Marguerre equations is used and the steady-state solutions are obtained by first applying the Galerkin method and then the harmonic balance method. Actual calculations are carried out for the square plate under the assumption of the three degrees-of-freedom system and the frequency response characteristics and typical waveforms are determined under various initial edge displacements including initially buckled cases. Effects of both initial deflection and initial edge displacement on the static deflection as well as the lower natural frequencies are also clarified.