Dynamics of Shells and Fluid-Loaded Plates.

This thesis is composed of two parts. The first part is concerned with wave propagation on elastic structures in vacuum. An asymptotic approximation is obtained for the dispersion relation of flexural waves propagating in an infinite, flat plate, with material and/or geometric properties periodic in one direction. A matrix approach is proposed to investigate waves in circular cylindrical thin shells joined with circular plates. Both the general propagator matrix and S-matrix formalisms are presented, with emphasis on the latter. The second part is devoted to structures with ambient fluid loading. The Green's function for a fluid-loaded plate under line loading is expressed as a sum of five fluid-loaded plate waves and an acoustic wave with magnitude given by an infinite integral, similar to a branch cut integral. A scattering matrix approach is presented to solve wave propagation problems on fluid-loaded plates with attached ribs. The low frequency asymptotic dispersion relation for a fluid-loaded plate with infinite number of equally spaced identical ribs is derived, from which an equation of motion for the plate is inferred which is valid also at low frequencies.