2022/06/20 by Elke Deckers, Deckers, Elke, Stijn Jonckheere +3
Engineering · #65F99 #65L99 #Acoustic Wave Phenomena Research #FOS: Mathematics #G.1.10 #G.1.3 #Numerical Analysis (math.NA) #Railway Engineering and Dynamics #Structural Health Monitoring Techniques
paper · pdf · doi:10.48550/arxiv.2206.09617
openalex publication_date 2022/06/20 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28
The analysis of sound and vibrations is often performed in the frequency domain, implying the assumption of steady-state behaviour and time-harmonic excitation. External excitations, however, may be transient rather than time-harmonic, requiring time-domain analysis. Some material properties, e.g. often used to represent for damping treatments, are still described in the frequency domain, which complicates simulation in time. In this paper, we present a method for the linearization of finite element models with nonlinear frequency dependencies. The linearization relies on the rational approximation of the finite element matrices by the AAA method. We introduce the Extended AAA method, which is classical AAA combined with a degree two polynomial term to capture the second order behaviour of the models. A filtering step is added for removing unstable poles.