Transient Response of a Point-Excited Submerged Spherical Shell

The transient responses of a submerged spherical shell to a concentrated impulse and Heaviside load are obtained by using the classical mode method and the Laplace transform. For long time solutions, only a relatively small number of modes are sufficient, while for the short time response, a large number of modes must be used in order to achieve acceptable accuracy. For the lower modes, the inversion integral involves only simple poles and can be evaluated by Cauchy’s residue theorem. For the higher modes it is necessary to use asymptotic approximations and the inversion involves branch points and poles. A spherical wave approximation, similar to Haywood’s cylindrical wave approximation, is also used to solve the transient problem. It is found that the approximation accurately predicts the maximum peak response for the impulse load, while it underestimates the response for the Heaviside load.