A Multi-Parameter Perturbation Solution and Experimental Verification for Bending Problem of Piezoelectric Cantilever Beams

Abstract

The existing studies indicate that the application of piezoelectric polymers is becoming more and more extensive, especially in the analysis and design of sensors or actuators, but the problems of piezoelectric structure are usually difficult to solve analytically due to the force–electric coupling characteristics. In this study, the bending problem of a piezoelectric cantilever beam was investigated via theoretical and experimental methods. First, the governing equations of the problem were established and non-dimensionalized. Three piezoelectric parameters were selected as perturbation parameters and the perturbation solution of the equations was finally obtained using a multi-parameter perturbation method. In addition, the relevant experiments of the piezoelectric cantilever beam were carried out, and the experimental results were in good agreement with the theoretical solutions. Based on the experimental results, the effect of piezoelectric properties on the bending deformation of piezoelectric cantilever beams was analyzed and discussed. The results indicated that the multi-parameter perturbation solution obtained in this study is effective and it may serve as a theoretical reference for the design of sensors or actuators made of piezoelectric polymers.

Functional Polymers in Sensors and Actuators: Fabrication and Analysis

“…The seventh contribution to the Special Issue focused on the bending problem of a piezoelectric cantilever beam via theoretical and experimental methods. Due to the extensive applications of piezoelectric polymers in the design of intelligent structures, including the sensors and actuators, Yang and associates from Chongqing University, proposed a method to deal with the challenge of solving the governing equations of these materials due to the force-electric coupling characteristics [6]. To do so, they derived the theoretical solution of the bending problem of piezoelectric cantilever beams by the multi-parameter perturbation method, which is a general analysis method for solving approximate solutions of non-linear mechanical problems.…”

Continuous Journey Toward Polymer Applications

“…While 3D printing, as a newly emerged technology, attracts attention from a lot of researchers as a method with which to explore new ways to fabricate polymeric devices with enhanced performance and/or new functions [1][2][3][4][5], sensors and actuators (including wearable/flexible electronic devices) still appear to be the major focus in polymer applications [1,[5][6][7][8][9][10][11][12][13][14][15]. Polymers with special features/functions, such as stimulus-responsive and shape memory [16,17], self-healing [18][19][20][21][22], and assembly [23][24][25][26][27] are being continuously developed, along with analytical/numerical studies [28][29][30], in order to capture the fundamentals for efficient and/or optimized engineering design. Of course, the above mentioned are only parts of the topics of the published papers in 2019 under this section, which focuses on polymer applications.…”