Free Damping Vibration of Piezoelectric Cantilever Beams: A Biparametric Perturbation Solution and Its Experimental Verification

Abstract

As an intelligent material, piezoelectric materials have been widely used in many intelligent fields, especially in the analysis and design of sensors and actuators; however, the vibration problems of the corresponding structures made of the piezoelectric materials are often difficult to solve analytically, because of their force−electric coupling characteristics. In this paper, the biparametric perturbation method was used to solve the free damping vibration problem of piezoelectric cantilever beams, and the perturbation solution of the problem solved here was given. A numerical example was given to discuss the influence of the piezoelectric properties on the vibration of piezoelectric cantilever beams. In addition, related vibration experiments of the piezoelectric cantilever beams were carried out, and the experimental results were in good agreement with the theoretical results. The results indicated that the biparametric perturbation solution obtained in this study is effective, and it may serve as a theoretical reference for the design of sensors and actuators made of piezoelectric materials.

Keywords

• free damping vibration
• cantilever beam
• piezoelectric materials
• biparametric perturbation method
• experimental verification