Model order reduction in structural dynamics

Abstract

Frequency response analysis in structural dynamics usually requires solving large dynamical systems of the form (-ω2M + iωD + K)u(ω) = f (ω), which result from a FE discretization. A straightforward solution of big systems requires a high computational cost; therefore several Model Order Reduction (MOR) techniques have been developed in the last decades to obtain faster and efficient results. Between them interpolatory approaches have gained importance for solving second order dynamical systems. This work presents and compares ten MOR techniques which are suitable for structural dynamics problems. These are: Guyan-Irons Reduction, Improved Reduction System, Dynamic Reduction, Real Modal Analysis, Complex Modal Analysis, Craig-Bampton Method, and Interpolatory MOR methods like Multi-point Padé Approximation, the Krylov-based Galerkin Projection and the Derivativebased Galerkin Projection. A brief summary of the theoretical background is presented for each method. A first numerical example shows the applicability for damped systems and a second example shows suitability of the Interpolatory MOR methods for industrial applications, using data from a commercial FE software (ANSYS®).