Nonlinear synthetic impedance circuits for piezoelectric structures

Abstract

Low-frequency applications of piezoelectric shunt circuits for vibration and noise attenuation triggered the research on implementing synthetic impedance circuits in smart structures a few decades ago. Most of the existing efforts have been limited to standard scenarios of emulating linear circuit components such as inductances by means of their synthetic circuit counterparts to avoid the use of large coils when targeting relatively low frequencies. Other examples have included the emulation of negative capacitance circuits in various applications, most recently for bandgap enhancement in locally resonant piezoelectric metamaterials and metastructures. In this work, we explore synthetic impedance circuitry emulating nonlinear relationship to use in conjunction with piezoelectric structures, particularly for vibration absorption. The focus is placed on nonlinear inductance development to realize Duffing-like behavior in the synthetic impedance circuit when combined with piezoelectric capacitance and dissipative (resistive) elements. Time-domain numerical simulations, approximate analytical modeling, and series of experiments are performed for comparison. Results are demonstrated on a piezoelectric cantilever shunted to such nonlinear circuits with different nonlinear parameters and excited under mechanical base motion.