External authors:

• Nicolas Torres-Ulloa ( Universidad de Chile )
• Erick Kracht ( Pontificia Universidad Catolica de Chile )
• Urban Fasel ( Imperial College London )

Abstract:

Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics represent spatial patterns in vibration, temperature, or velocity fields associated with simple time dynamics. However, for systems that depend on one or more parameters, eigenmodes obtained for one set of parameter values are not necessarily dynamically relevant in other regions of parameter space. In this work, we formulate a method to obtain an optimal orthogonal basis of eigen-deformation modes (EDMs) that capture eigenmode variations across a range of parameter values. Through numerical examples of common parameterized dynamical systems in engineering, we show that EDMs provide physical insight into the effects of parameter changes on the underlying dynamics. Furthermore, we expect the approach to enable parameterized nonlinear model reduction techniques that rely on accurate, yet low-dimensional, representations of parameter-dependent eigenspaces.