Structural and Multidisciplinary Optimization

, Volume 43, Issue 4, pp 495–517 | Cite as

A Krylov–Arnoldi reduced order modelling framework for efficient, fully coupled, structural–acoustic optimization

  • R. Srinivasan Puri
  • Denise Morrey
Research Paper


In this work, a reduced order multidisciplinary optimization procedure is developed to enable efficient, low frequency, undamped and damped, fully coupled, structural–acoustic optimization of interior cavities backed by flexible structural systems. This new method does not require the solution of traditional eigen value based problems to reduce computational time during optimization, but are instead based on computation of Arnoldi vectors belonging to the induced Krylov Subspaces. The key idea of constructing such a reduced order model is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the noise transfer function of the coupled system. In a unified approach, the validity of the optimization framework is demonstrated on a constrained composite plate/prism cavity coupled system. For the fully coupled, vibro–acoustic, unconstrained optimization problem, the design variables take the form of stacking sequences of a composite structure enclosing the acoustic cavity. The goal of the optimization is to reduce sound pressure levels at the driver’s ear location. It is shown that by incorporating the reduced order modelling procedure within the optimization framework, a significant reduction in computational time can be obtained, without any loss of accuracy—when compared to the direct method. The method could prove as a valuable tool to analyze and optimize complex coupled structural–acoustic systems, where, in addition to fast analysis, a fine frequency resolution is often required.


Krylov subspace Arnoldi Structural–acoustic optimization Mesh adaptive direct search 



The authors wish to acknowledge the Engineering and Physical Sciences Research Council (EPSRC GR/S27245/01) for the grant project under which this research was carried out. The authors also acknowledge the support of Jeffrey L. Cipolla (Simulia Corporation formerly ABAQUS Inc.), T. Bharj (Ford Motor Company, UK), M. Birrell (BI-Composites, UK), R Davidson (Crompton Technology, UK), M. Collier (Hodgson and Hodgson, UK), A. Atkins (Siemen’s Magnet Technology, UK) and M. Burnett (Motor Industry Research Association, UK) who were industrial collaborators in the project.


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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of TechnologyOxford Brookes UniversityOxfordUK

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