The Natural Frequency of Vibration of Curved Rectangular Plates

Abstract

SummaryThe natural frequency of vibration of curved rectangular plates, with both simply-supported and fixed edges, is evaluated for the fundamental extensional mode. This mode is thought to be applicable when the plates are excited by a uniformly distributed pressure as may occur with a dynamic pressure wave. The natural frequencies corresponding to this mode increase fairly rapidly with the curvature of the plate.The natural frequency of vibration of the plates when the mode is the fundamental inextensional mode is also considered. The frequency of this mode is higher than that of the extensional mode for small curvatures, but the inextensional mode frequency falls slowly with increase in curvature of the plate. Thus, if the curvature of the plate is sufficiently large, the frequency of the fundamental inextensional mode is lower than that of the extensional mode.