Vibration theory of piezoelectric plate with gradient thickness to frequency programmable design

Abstract

In today’s smart device applications, optimizing the properties and designing characteristics of piezoelectric materials is critical. This paper derives vibration theory of piezoelectric plate with gradient (stepped/continuous) thickness and investigates their mechanical–electrical coupling mechanism during vibration and the resonance behavior. With this theory, we have established the mapping relationship between the radius, thickness distribution, and intrinsic frequency of a piezoelectric plate with gradient thickness. It is a challenge to solve the multi-parameter inversion problem, determining the structural radius and thickness distribution through a given frequency. In this paper, a self-learning optimization loop algorithm is used to determine the frequency response ranges for variable-thickness plates with different radii, enabling rapid design for target frequencies. Subsequently, the theory is validated through a full-field scanning laser vibrometer experiment, with error for the first seven orders of the intrinsic frequency are ranges from 0.4% and 5%. This study presents a scheme for the frequency forward design of piezoelectric thin plates and demonstrate an interesting case of tone scale design. By thoroughly investigating the mechanical–electrical coupling mechanism of piezoelectric plate with gradient thickness during vibration, it is expected that this study will not only reveal its complex physical phenomena, but also provide a theoretical basis for optimal design.