Chapter 12 Expansion of Coupled Structural-Acoustic Systems Ryan Schultz, Dagny Beale, and Ryan Romeo Abstract Expansion is useful for predicting response of un-instrumented locations and has traditionally been applied to structures alone. However, there are a range of hollow structures where the influence of the acoustic cavity affects the structural response, and the structural response affects the acoustic response. This structural-acoustic coupling results in a gyroscopically coupled system with complex modes. Though more complicated than modes of a structure alone, the modes of the coupled structural-acoustic system can be used as the basis vectors in an expansion process. In this work, complex modes of a model of a coupled structural-acoustic system are used to expand from a sparse set of structural and acoustic response degrees of freedom to a larger set of both structural and acoustic degrees of freedom. The expansion technique is demonstrated with a finite element model of a hollow cylinder with simulated displacement and pressure measurements, and expansion is studied for both modal and transient responses. Though more nuanced than traditional structure-only expansion problems, the displacement and pressure response of a coupled structural-acoustic system can be expanded using the coupledsystem modes. Keywords Expansion · Coupled system · Acoustoelastic · Structural-acoustic · Modes 12.1 Motivation and Theory One major challenge in experimental testing is that only a few discrete points on an object of interest are measured but the response of the full object is usually desired. Expansion is a method that can take the limited number of measurements and some knowledge of the mode shapes of the object to predict the response at a larger number of points, and is especially useful for structures with components that cannot easily be measured. Traditionally, expansion has only been applied to solid structures with mode shapes comprised of displacement, velocity, or acceleration responses. However, there are many objects of interest that are hollow structures that contain an acoustic cavity, such as rocket fairings and automobiles. The responses of these coupled structural-acoustic systems depend on both structural modes and acoustic pressure modes. This work applies traditional expansion to a coupled system to show that expansion is possible in coupled structures, and to determine the challenges unique to coupled expansion. Expansion from a set of measurements at the a-DOF to a set of unmeasured responses at the n-DOF is achieved by multiplying the measured responses, {xa}, by a transformation matrix, [T], as in Eq. 12.1. {xn}=[T] {xa}. (12.1) Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. R. Schultz ( ) · D. Beale · R. Romeo Sandia National Laboratories, Albuquerque, NM, USA e-mail: rschult@sandia.gov © The Society for Experimental Mechanics, Inc. 2021 B. Dilworth (ed.), Topics in Modal Analysis & Testing, Volume 8, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47717-2_12 131
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