Dynamic Problems in Isotropic Plates

Abstract

Plates found in applications are often subject to dynamic loads. These loads can be directly applied to the plate (i.e., wave impact, wind gusts, blast overpressure, impact by birds or other objects, etc.). In numerous applications, dynamic loads are applied to the plate by unbalanced rotating machinery supported by the plate or through the kinematic excitation by beams that support both the plate and the engine. In all these problems, the structural integrity of the plate has to be analyzed to prevent immediate failure due to excessive dynamic stresses or fatigue damage as a result of continuous large-amplitude vibrations. The present chapter provides an insight into vibrations of isotropic plates, including free and forced vibrations, response to non-harmonic dynamic loads, large-amplitude vibrations and dynamic instability. Dynamic problems of composite plates that can be investigated using an extension of analytical and numerical tools employed for the analysis of their isotropic counterparts are outside the scope of this book. An exception applicable to the analysis of composite plates is vibration of plates reinforced with stringers whose constitutive equations and equations of motion resemble those of composite plates (Sect. 4.5).