CAM Colloquium - Alex Vakakis: Nonlinear Sonic Vacua

Friday, October 30, 2015
We will present recent results on a special class of dynamical systems designated as nonlinear sonic vacua. These systems are non-linearizable, and have zero speed of sound (in the sense of classical acoustics). Accordingly, their dynamics and acoustics are highly degenerate and tunable with energy, enabling new and highly complex nonlinear phenomena. Two examples of sonic vacua will be discussed. The first is un-compressed ordered granular media, which, depending on their local state, behave either as strongly nonlinear and non-smooth dynamical systems (in the absence of strong local compression), or as almost linear coupled oscillators (under strong local compression, e.g., in the primary fronts of propagating solitary pulses). Analytical techniques for predicting the strongly nonlinear properties of these media will be discussed. The second example concerns a spring-mass lattice in the plane. In the small energy limit this seemingly simple system is “transformed” by geometric nonlinearity to a nonlinear sonic vacuum with surprising properties, such as strong nonlocality (despite of only next-neighbor interactions in the lattice!), orthogonal nonlinear normal modes, and accelerating propagating fronts. Interesting applications of nonlinear sonic vacua will be discussed, including intense energy cascading from low-to-high frequencies and long-to-short wavelengths, resembling 'mechanical turbulence'.

Bio
Alexander F. Vakakis received his Ph.D. in Applied Mechanics from the California Institute of Technology (1990), an M.Sc. from Imperial College, London (1985), and a Diploma in Mechanical Engineering from the University of Patras, Greece (1984). He has been faculty at the University of Illinois since 1990, with an eight- year break when he was faculty at the National Technical University of Athens (2000-08). Currently he serves as Associate Editor of the ASME Journal of Applied Mechanics and of Meccanica. He is a Fellow of ASME, and the recipient of the Thomas Bernard Hall Prize (2012) and the PE Publishing Award (2009), both from the UK Institution of Mechanical Engineers. In 2014 he received the ASME Applied Mechanics Division Thomas Caughey Award in Nonlinear Dynamics. Among other topics his current research work includes dynamics, vibrations and acoustics; nonlinear system identification, reduced-order modeling and model updating; acoustic metamaterials; nonlinear micro- and nano-resonators; control of fluid-structure interactions and aeroelastic flutter; and nonlinear vibration energy harvesters.