An analogue twin for piezoelectric vibration damping of multiple nonlinear resonances

Abstract The objective of this study is to extend the concept of analogous piezoelectric networks to vibration mitigation of multiple nonlinear resonances. First, the undamped linear part of the electrical network is designed so as to possess similar modal characteristics as those of the underlying linear mechanical structure. Then, nonlinear electrical components possessing the same mathematical form as that of the mechanical nonlinearities are added to the network. Because both modal and nonlinear analogies are enforced, the electrical network can be seen as an analogue twin of the mechanical structure. When the network is coupled to the structure via an array of piezoelectric elements, it is shown numerically and experimentally that such an analogue twin offers important benefits for vibration mitigation over a broad range of frequencies and excitation amplitudes.