A general time-domain approach is presented to address the transient vibratory response of fluid-loaded plates or shells of arbitrary shape with attached substructures when subjected to specified mechanical and/or acoustical excitations. The approach is based on utilizing an in vacuo eigenvector expansion with time-dependent coefficients to describe the velocity field of the basic structure. Fluid loading and the effect of the substructures on the basic structure are described via the use of convolution integrals involving the modal velocity coefficients and impulse responses. A universal set of coupled convolution integral equations for the time-dependent modal velocity coefficients of the basic structure are developed using a time-domain method of analysis. Special cases, which include a finite plate and a general shell of revolution, are addressed. A reduced set of the coupled convolution integral equations for the time-dependent modal velocity coefficients is obtained for the plate, and sets of similar equations are also obtained for the shell. Numerical results are presented and discussed for some simple beam, plate, and shell problems involving transient excitations.