A piezoelectric nonlinear energy sink shunt for vibration damping

The theoretical study and experimental validation of a nonlinear shunt circuit for piezoelectric vibration damping is investigated here. The circuit consists of a resistor, an inductor and a nonlinear cubic voltage source. The shunt acts as an electrical analog to the mechanical nonlinear energy sinks (NESs). These mechanical NESs are passive vibration absorbers that typically have a cubic nonlinear stiffness. They have attractive properties such as saturation of the host system’s vibration amplitude and strongly modulated response. This increases its operational frequency bandwidth and robustness against variations in the properties of host systems compared to linear vibration absorbers. However, the nonlinear nature may induce isolated responses in the host system that induce high vibration amplitudes. This paper investigates if these attractive properties also occur in the electric nonlinear energy sink shunt. An analytical expression for the frequency response is derived through the complexification-averaging method. Bifurcations in the frequency response reveal the occurrence of a quasi-periodic vibration energy exchange between the host system and the voltage over the electrodes of piezoelectric material. This is the main mechanism behind the amplitude saturation of the host system. Other bifurcations also reveal the existence of isolated responses. The nonlinear shunt is then realized with analog multipliers and a synthetic inductor and its performance in vibration damping is experimentally verified for a cantilever beam.

Recommended citation: Kevin Dekemele, Christophe Giraud-Audine, and Olivier Thomas. "A piezoelectric nonlinear energy sink shunt for vibration damping." Mechanical Systems and Signal Processing 220 (2024): 111615.
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