Structural-acoustic analysis of 3-D curved shell with a discontinuity using analytical/numerical matching (ANM)

Abstract

Analytical/numerical matching (ANM) is used to determine the structural vibration of a curved shell driven at a single support. The ANM solution decomposes the problem into global, local, and matching subproblems. The global problem addresses large-scale effects with structural discontinuities replaced by smooth distributed forces. The local problem models the rapidly changing region around a structural discontinuity. These constituent problems are solved independently by the most efficient method available. Here, the local problem is solved numerically using 3-D solid finite element analysis (FEA) and the matching problem is solved analytically, using the Love–Timoshenko shell equations. The global problem is decomposed modally in azimuth, leaving a corresponding FEA problem in the axial direction for each mode. Due to the smoothness of the global problem, relatively few modes are required for the modal decomposition and the affiliated FEA problem can be solved using a low resolution. An advantage of the ANM method is its ability to capture the detailed response of structures with geometric complexities without having to incorporate the complexity (via higher-order elements or high mesh densities) in the modeling of the large global problem. [Work sponsored by ONR.]