Complex modal decomposition
for traveling waves 
and nonsynchronous oscillations 

Abstract:

We introduce synchronous and nonsynchronous modes in vibration systems, and the use of complex modes for describing nonsynchronous motions, for example traveling waves.  We then briefly review proper orthogonal decomposition (POD), which is a common tool for the extraction of real “energy modes” in spatiotemporal systems.  Some generalizations of POD that enable extractions of complex modes are then presented.  Illustrative examples of these tools shown, including the application of a state-variable modal decomposition to an end-damped beam, and the application of complex orthogonal decomposition to structures and bio-locomotion.

Biography:

Brian Feeny is a Professor in the Department of Mechanical Engineering at Michigan State University.  He obtained his PhD at Cornell University, and held a postdoc at ETH in Zurich.  He is a Fellow of the American Society of Mechanical Engineers (ASME), for which he has served as chair of the Technical Committee on Vibration and Sound, as an associate editor (JVA and JCND), and now as secretary for the Design Engineering Division Executive Committee.  He directs his department’s student exchange program between MSU and RWTH Aachen.  His research activities include modal decomposition, parametric systems, nonlinear vibrations, and vibration with friction, with applications to wind turbine blade vibration, pendulum vibration absorbers, and bio-locomotion.