Orthocomplement reduced order models for strongly coupled structural-acoustic systems

Abstract

Despite the enormous strides in computing power, reduced-order models (ROMs) remain essential for design optimization and early stage design. The energetically optimal basis for ROMs of vibroacoustic systems derives from the coupled Eigen problem: no basis of smaller dimension contains a greater amount of system energy. While vital, this L2-type framework is also insufficiently accurate on a pointwise basis for many problems. A simply supported beam with a point load is an obvious thought experiment: the smooth modal functions converge to the correct displaced shape very slowly. The well-known “residual mode” or orthocomplement concept overcomes this problem, by augmenting the space of modal functions with static solutions to the point loads. These new residual modes are orthogonalized against the modal space, and used otherwise conventionally. This work describes the development of ROMs of submerged structures by extending the residual mode approach to the strongly coupled structural-acoustic case. We derive methods to use these ROMs in substructures. Numerical examples show that the structural acoustic residual mode formulation is very effective in improving the solution method in the low-frequency limit, especially in the fluid, and also at the high-frequency limit, where response quantities tend to the average of the direct-solve FEM response.