Combined Direct/Adjoint Reduced-Order Approximations for Design-Oriented Structural-Acoustics

Abstract

The accuracy of modal-order reduction methods in structural dynamics and structural acoustics depends on the particular problem analyzed and particular modal bases selected. Modal-order reduction methods can become quite inaccurate when sensitivities of response functions with respect to design variables are required. Past research in linear aerodynamics and structural dynamics had shown how direct and adjoint solutions can be combined to yield reduced-order analysis and sensitivity approximations of the problems at hand with second-order accuracy. Efforts are reported to extend the methodology to structural acoustic problems of fluid-filled cavities enclosed by flexible walls. In this case, stress and pressure response to excitation has to be evaluated over a range of frequencies. Improved and more consistent accuracy is reported over a range of frequencies with the second-order method when accuracy of both approximate direct and approximate adjoint solutions is comparable. The second-order method cannot improve accuracy of first-order methods in general when one of the approximate first-order solutions is highly inaccurate.