3 Case studies of model order reduction for acoustics and vibrations

This chapter presents several case studies to illustrate specific aspects in setting up reduced-order models of acoustic and vibration models in mechanical applications. Modal truncation approaches have been a provenworkhorse for over half a century in civil andmechanical engineering, but, formany (recent) applications, these techniques are too limited. Inmechanical engineering,model users are interested in a range ofmodel applications: frequency and time domain, linear and nonlinear, single domain and multiphysics, etc. This broad range of applications makes it particularly challenging to devise appropriate reduced-order model schemes, as a scheme for one model use might be completely inadequate for other applications. Krylov methods for example have been a go-to technique inmany domains, but face particular challenges in mechanical finite element models as the system’s eigenvalues lie along the imaginary axis and the high frequencies are irrelevant for a givenmesh size from a physical perspective. In the current chapter we explore these particularities for different types of mechanical models and simulation purposes, in order to surface several good practices and points of attention when applying model order reduction on these models. We bring together two different viewpoints: the application of model order reduction from a purely mathematical point of view and the physical interpretation of models and expected properties of reduced-order models based on physical arguments from the field of mechanics. While we touch upon a range of novel model order reduction techniques, we do not discuss parametric model order reduction as it is expected that the presented guidelines can be exploited in parametric problems without additional specific concerns.