Digitally programmable nonlinear energy sink via essentially nonlinear synthetic impedance circuit

An essentially nonlinear digitally programmable shunt circuit is explored in this work for the practical realization of nonlinear energy sink (NES) behavior in piezoelectric structures. The NES allows for energy transfer from the host structure to the nonlinear attachment in an irreversible fashion as well established. The main advantage of a NES is its ability to absorb vibrations over a broad frequency bandwidth since it has no preferential resonance, i.e., it is not tuned to any specific linear resonance frequency. In this work, a synthetic impedance circuit is employed for the emulation of a nonlinear inductor connected in parallel to a resistor, providing digital analogous of essential stiffness nonlinearity and damping, respectively, while piezoelectric capacitance acts as the mass analogue. Model simulations are conducted first to identify the suitable parameters of the synthetic impedance circuit in order to guide the experiments. The performance of the piezoelectric NES is then validated experimentally for a geometrically linear piezoelectric cantilever shunted to a programmable essentially nonlinear inductance circuit. Unlike the analog circuit explored in the literature using nonlinear capacitance (hence requiring negative capacitance in the circuit to make it essentially nonlinear), this work is inductive type (does not require negative capacitance) and is entirely programmable with digital control.