Bistable attachments for wideband nonlinear vibration attenuation in a metamaterial beam

This work investigates the amplitude-dependent dynamics of a locally resonant metamaterial beam with bistable attachments. The concept that was previously demonstrated for a discrete chain is extended to a continuous system, and the enhancement in vibration attenuation bandwidth is investigated through a cantilever beam under base excitation. The analysis approach combines the harmonic balance method and time-domain numerical integration to capture periodic and aperiodic responses for up-sweep and down-sweep harmonic excitation. The bistable attachments are shown to exhibit linear intrawell, nonlinear intrawell and nonlinear interwell oscillations for low, moderate, and high base acceleration levels. As a result, the metastructure leverages linear locally resonant bandgap under low excitation intensity, and nonlinear wideband attenuation due to chaotic vibrations of the bistable attachments under high excitation intensity. This is first demonstrated through frequency sweep numerical simulations for a broad range of excitation amplitudes. Experimental validations are then presented for a base-excited cantilever beam hosting seven magnetoelastic beam attachments. For moderate-to-high amplitude excitation levels, the interwell oscillations of the attachments produce an attenuation frequency range that is 350% wider than the corresponding linear locally resonant bandgap (observed for low-amplitude excitation levels), yielding the suppression of modes outside the bandgap with increased excitation intensity.