Piezoelectric and magnetostrictive materials exhibit high energy densities and broadband drive capabilities enabling compact actuator designs. These applications include acoustic transducers, nano-positioning systems such as Atomic Force Microscopes (AFM) and other smart actuators for precise control of displacement. However, these materials exhibit hysteresis and constitutive nonlinearities at all drive levels. Quantification and understanding these effects on the frequency domain behavior of the materials is necessary for precise control of displacement as well as developing control strategies to alleviate the higher harmonics produced during operation. Whereas considerable effort has been made on model development and understanding these materials in parameter space and time domain, a comprehensive understanding in frequency domain is lacking. Here we quantify the effect of hysteresis, nonlinearities, bias fields and AC drive levels on the frequency domain behavior.

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