Faster frequency sweep methods for structural vibration and acoustics analyses

Abstract

The design of large, complex structures typically requires knowledge of the mode shape and forced response near major resonances to ensure deflection, vibration, and the resulting stress are kept below acceptable levels, and to guide design changes where necessary. Finite element analysis (FEA) is commonly used to predict Frequency Response Functions (FRF) of the structure. However, as the complexity and detail of the structure grows, the system matrices, and the computational resources needed to solve them, get large. Furthermore, the need to use small frequency steps to accurately capture the resonant response peaks can drive up the number of FRF calculations required. Thus, the FRF calculation can be computationally expensive for large structural systems. Several approaches have been proposed that can significantly accelerate the overall process by approximating the frequency dependent response. Approximation approaches based on Krylov Galerkin Projection (KGP) and Pade calculate the forced response at only a few frequencies, then use the response and its derivatives to reconstruct the FRF in-between the selected direct calculation points. This paper first validates the two approaches with analytic solutions for a simply supported plate, and then benchmarks several numerical examples to demonstrate the accuracy and efficiency of the new approximate methods.