| This dissertation is a theoretical investigation of the vibration of an infinite, compliant layer, attached on one side to a steel plate, flush with a half space of water on the other. Vibration is induced by a line force with harmonic time dependence applied to the plate. Response of the compliant layer is computed.;This structure is a simplified representation of the hull of a submarine that is coated with a vibration-damping layer. Concern is with noise from the hull that propagates through the damping layer.;Bernoulli theory is used for the plate, elasticity theory is used for the compliant layer, and acoustic radiation occurs in seawater. Computer software, Mathematica, is used to solve the system of equations. Results are presented in plots of compliance against wavenumber and frequency, of compliance against complex wavenumber, and of displacement against position in the layer.;Forced vibration of the three-medium structure is compared to free vibration of an isolated, uncoupled plate, of an isolated elastic layer waveguide, and of a pair consisting of isolated dilatational and shear waveguides. Behavior of the uncoupled, isolated components can be recognized in the behavior of the intercoupled three-medium structure. Elastic layer waveguide modes and plate bending modes occur at wavenumber and frequency values nearly the same as those for which the entire structure resonates. This means that aspects of the complicated behavior of the complete system can be understood, and even computed, in terms of the behavior of simpler subsystems.;Vibration of the system with dissipation in the coating layer is compared to that without dissipation. Dissipation eliminates resonance associated with elastic waveguide modes, while leaving resonance associated with the plate nearly unaffected.;At the coating-water interface, tangential vibration is larger, by about an order magnitude, than normal vibration. Furthermore, from the plate to the water, through the coating, there is an amplification of tangential vibration, even through a dissipative coating. |
