Steady-state motion of a plate with a discontinuous mass

An “exact” solution employing the normal mode approach is presented for the steady-state motion of a plate of arbitrary shape and with arbitrary boundary conditions that is provided with a discontinuous mass. The plate is viscously damped and the excitation is furnished in the form of distributed and/or concentrated loads that vary sinusoidally. The rigid mass, which may act as a vibration damper, can be applied to any point in the structure. Experimental studies with a mechanical model corroborate the theoretical results. Results of the analysis are applied to cantilever and simply-supported square plates subjected to base excitation and discrete loads. The effects of all system parameters, including damper location and mass ratio, mode shapes, viscous damping, and excitation frequency are determined. It is found that the system under consideration is an efficient device for reducing the vibration of plates, particularly cantilevered ones.