Benjamin M. Goldsberry, Andrew N. Norris, Samuel P. Wallen, Michael R. Haberman
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Green's Function Approach to Model Vibrations of Beams with Spatiotemporally Modulated Properties
The forced time harmonic response of a spatiotemporally-modulated elastic
beam of finite length with light damping is derived using a novel Green's
function approach. Closed-form solutions are found that highlight unique mode
coupling effects that are induced by spatiotemporal modulation, such as split
resonances that are tunable with the modulation parameters. These effects of
order unity are caused by spatiotemporal modulation with small amplitude
appropriately scaled to the magnitude of the light damping. The scalings
identified here between the modulation amplitude, the damping, and the inner
range of frequency near the modified resonances, translate over to more
complicated and higher dimensional elastic systems.