Green’s function approach to model vibrations of beams with spatio-temporally modulated properties

The forced time harmonic response of a spatio-temporally 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 spatio-temporal modulation, such as split resonances that are tunable with the modulation parameters. These effects of order unity are caused by spatio-temporal modulation with a small amplitude appropriately scaled to the magnitude of the light damping. The scalings identified here between the modulation amplitude, the damping and the inner frequency range near the modified resonances, translate over to more complicated and higher dimensional elastic systems.