Effect of substructures on the vibration of fluid-loaded shells

The vibration response of submerged elastic shells with internal substructures is examined using modal based methods. The analysis involves the shell surface displacements and pressure fields as well as the radiated acoustic field. The analysis is carried out for axisymmetric shells of both infinite and finite lengths.;The 2-D response of infinitely long cylindrical shells is studied for the cases that the internal substructures consist of either an oscillator or continuous structures. The analysis begins with a Lagrange formulation where conditions at the connection points of the substructures are taken into account by the use of Lagrange multipliers. The formulation results in an expression for the Lagrange multipliers in terms of an infinite sum of rational polynomials. In a prescribed frequency range, approximate solutions are obtained by using the frequency window method. The method separates the infinite sum into two parts, retains mathematical detail for terms with poles within a frequency window, and approximates the remaining terms. Since the terms within the window give rise to the important resonance effects, the most important aspects of the dynamic behavior of the system are preserved.;The analysis is then extended to axisymmetric shells of finite length. For this non-separable geometry, a variational analysis is combined with the use of the Lagrange formulation since a closed form analytical solution for the acoustic field is not available. The resulting system of equations is solved to simultaneously obtain a solution for the shell/substructure displacement field and the shell surface pressure. A singularity decomposition is used to extract the dominant part of the shell response for a given frequency window. This is accomplished by determining the response singularities of the fluid/shell system which lie close to the real axis of the complex frequency plane. The response can then be expressed in terms of these singularities and a residual term which approximates all other contributions. Once the singularities of the fluid/shell system have been established for a given frequency window, a highly accurate estimate of the response of the fluid/shell/sub-structure system can be computed with relative ease for different substructure and loading configurations. Far-field pressure is then determined by application of the Helmholtz-Kirchhoff integral theorem.;For all the configurations studied, it is found that the presence of substructures has significant effects on the dynamic response of the shells. These effects can be accurately predicted by the frequency window method.