Demonstrating wave and vibrational behavior in spatiotemporally modulated systems

Elastic materials with time and space varying properties are interesting candidates to control bulk and guided waves in unprecedented ways which include nonreciprocal transmission, unidirectional mode conversion, mode coupling, and frequency conversion. Previous work on elastic waves in spatiotemporally modulated (STM) media have focused on nonreciprocal vibrations of finite domains with modulated stiffness. Less attention has been given to the modulation of impedance boundary conditions of finite structures or at interfaces between domains. This work investigates elastic wave behavior at boundaries with modulated impedances. The boundary impedance is represented using a lumped parameter mass spring damper system with a spring having a temporally modulated stiffness. The effective input impedance is modeled using direct numerical simulation and a semi-analytical Fourier series expansion model. The models are compared to experiments on a base-excited cantilevered Euler-Bernoulli beam with modulated effective stiffness via piezoelectric patches with temporally varying electric shunting circuits. [Work supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics and by the Office of Naval Research under Award N00014-23-1-2660.]