Nonlinear Dynamics of Multiphysics Systems

It is well known that viscous damping can destabilize non-conservative autonomous systems, a phenomenon known as Ziegler's paradox. In contrast, in non-autonomous systems subjected to parametric excitation, viscous damping generally increases the threshold for parametric resonance when the modal frequencies are not closely spaced. We investigate the role of damping in parametrically excited systems in a multiphysics system with closely spaced modal frequencies, which consists of a rotating cantilever piezoelectric beam periodically plucking a stationary cantilever piezoelectric beam through the magnetoelastic interaction between magnets attached to the tips of the beams. Numerical simulations using empirically identified parameters reveal that damping can have opposite effects on resonance: increasing the damping in the bending mode of the stationary beam suppresses its resonance, whereas increasing the damping in the bending mode of the rotating beam amplifies it. We also conduct experiments to verify both the dampening and amplification effects. Potential applications include rotary energy harvesting and vibrating structure gyroscope.

Select publications

1. Tai, W. C., & Mukherjee, R. (2026). Amplification effect of damping in parametrically excited systems. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (submitted). American Society of Mechanical Engineers.

2. Tai, W. C. (2025). Damping-destabilized parametric resonances of a rotating beam magnetically plucking a stationary beam. Journal of Sound and Vibration, 597, 118798.

3. Tai, W. C. (2023). Instability and parametric amplification of a piezoelectric energy harvester periodically plucked by a rotating magnet. Journal of Vibration and Acoustics, 145(4), 041003.