Nonlinear Flexural Vibrations of a Clamped Circular Plate

Abstract

Nonlinear flexural vibration of a circular plate clamped at its edge are investigated both experimentally and theoretically. The investigation has been restricted to the first axisymmetric mode. The time-dependent part of the nonlinear plate equations are reduced to Duffing’s equation by applying a one-term Ritz-Galerkin’s procedure. Test results are in good agreement with the theoretical calculations which indicate a non-linearity of hardening type for large amplitude vibrations. The period of vibration decreases by 35 percent when the amplitude is twice the thickness of the plate. The “jumps” in the amplitude-frequency response curves are observed to occur during a transition of a few seconds and are accompanied by a beating phenomenon.