A closed form solution for the dynamic response of finite ribbed plates

Abstract

A simple and closed form solution for the vibration response of finite ribbed plates to point force/moment excitations is presented in this paper. This solution shows that input mobilities of finite ribbed plates are bounded by the input mobilities of the uncoupled plate and beam that form the ribbed plate. It is found that point force input mobilities of a finite ribbed plate are controlled by the plate bending stiffness when the excitation force is more than a quarter wavelength away from the beam. The input mobilities are mainly dominated by the beam flexural stiffness when the force acts on or very close to the beam, and when the beam flexural stiffness is far greater than the plate bending stiffness. A similar result is found in the moment excitation case when the moment axis is perpendicular to the beam neutral axis (bending moment excitation). In contrast, the input mobilities of the ribbed plate do not vary much from that of the corresponding uncoupled plate when the moment axis parallels to the beam’s neutral axis (torsional moment excitation) where the input mobilities are mainly dominated by the plate bending stiffness. The reductions in plate kinetic energy due to beam insertions are discussed.