Dynamic Buckling of Thin Elastic Plates

Abstract

Abstract The behavior of thin elastic plates under loading parallel to their middle plane, constant or arbitrarily varying with time, is considered. The effect of vibrations in the middle plane is examined. In the transverse direction it is shown that by introducing appropriate nondimensional variables and parameters the time dependence reduces to the same type of equation as in the case of columns. Thus the fundamental features of plates and columns are similar. Additional discussion and examples of the solution of the nondimensional equation are presented. Higher modes are related to the fundamental mode of the same plate under appropriate different loading. The need of considering the entire time history of the loading is shown by examples. Shear loading and various boundary conditions are discussed. For loading constant during the time of application initially curved and eccentrically loaded plates are proved equivalent models for the investigation. A slight modification is necessary for a load arbitrarily varying with time.