Nonlinear Vibration of Buckled Beams and Plates

摘要

The purpose of the present study is to examine the theoretical response and stability of free and forced vibration of a simply supported, buckled, beam and rectangular plate. The equations of motion dealing with the buckled position in multiple degrees of freedom include the effect of an initial displacement caused either by initial axial load or by initial temperature. By assumed mode solution, two types of vibration are investigated: snap-through vibration (symmetrical vibration) and one-side vibration (unsymmetrical vibration). A small perturbation yields the Hill or Mathieu type of differential equation for stability investigation. Since the equations are coupled through the nonlinear term the excitation of one particular mode may feed some of its energy into other modes and cause the rest modes to vibrate. Thus this study examines not only the response and stability of the excited mode but also the response and stability of the rest modes. (Author)