A nonlinear piezoelectric shunt absorber with tunable piecewise linear negative capacitance

Abstract

In recent years, extensive research has been devoted to nonlinear piezoelectric shunt circuits for mitigating structural vibrations. However, existing studies have primarily concentrated on polynomial nonlinearity, particularly cubic nonlinearity. This paper develops a tunable non-smooth piezoelectric shunt absorber to suppress structural vibrations under harmonic excitation. We enhance the conventional resonant circuit by introducing a piecewise linear negative capacitor, which is implemented using a pair of diodes and voltage sources. The stationary response of the non-smooth system is derived using the complexification-averaging method. The effects of critical voltage and excitation intensity on the damping performance are investigated subsequently. Furthermore, we apply an adaptive control method based on the gradient descent algorithm with adaptive moment estimation (Adam) to the nonlinear circuit, improving its damping performance and enabling adaptation to changes in excitation intensity. Experimental results validate the effectiveness of the proposed adaptive nonlinear circuit, demonstrating superior stationary performance compared to linear resonant shunt circuits across a broad bandwidth of frequencies, especially at off-resonant frequencies.