Analytical modeling of PWAS in-plane and out-of-plane electromechanical impedance spectroscopy (EMIS)

Abstract

This paper discusses theoretical analysis of electro-mechanical impedance spectroscopy (EMIS) of piezoelectric wafer active sensor (PWAS). Both free and constrained PWAS EMIS models are developed for in-plane (lengthwise) and outof plane (thickness wise) mode. The paper starts with the general piezoelectric constitutive equations that express the linear relation between stress, strain, electric field and electric displacement. This is followed by the PWAS EMIS models with two assumptions: 1) constant electric displacement in thickness direction (D3) for out-of-plane mode; 2) constant electric field in thickness direction (E3) for in-plane mode. The effects of these assumptions on the free PWAS in-plane and out-of-plane EMIS models are studied and compared. The effects of internal damping of PWAS are considered in the analytical EMIS models. The analytical EMIS models are verified by Coupled Field Finite Element Method (CF-FEM) simulations and by experimental measurements. The extent of the agreement between the analytical and experimental EMIS results is discussed. The paper ends with summary, conclusions, and suggestions for future work.