Nonlinear piezoelectric resonance: A theoretically rigorous approachto constant I − V measurements

Methods for piezoelectric characterization include the standard resonance test. At higher powers, however, the material's inherent nonlinearity acts to significantly affect the expected resonance response. High-power resonance methods have previously been developed to describe piezoelectric nonlinearity. In this article we specify and describe the approximations adopted in the current theory and propose a more rigorous theory derived from fundamental principles. We first use thermodynamics to derive the form of the constitutive equations. In particular, we propose that the envelope rather than instantaneous values of stress, strain, and electric field must appear in these equations to yield a type of nonlinearity which, nonetheless, yields a sinusoidal current for sinusoid applied voltage. An alternative approach is set out describing the highly nonlinear experimental data by fitting just one adjustable material parameter to the entire impedance response measured around resonance. Theoretical descriptions for conventional constant-voltage and modified constant-current excitation are developed and compared with experiments for soft and hard compositions of a piezoelectric ceramic (PZT-5H and PZT-4D). The theory is able to match whole families of constant-voltage and constant-current curves with only one adjustable parameter. These models may be used to characterize the high-power properties of piezoelectric materials.