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.
Highlights
Piezoelectric polymers have been widely used in sensors, actuators, electronic information and intelligent structures because of its great force–electric coupling characteristics [1,2,3,4,5,6]
The piezoelectric polymers usually participate in the work of piezoelectric instruments in the form of piezoelectric sheets which usually are simplified to a piezoelectric cantilever beam [7,8,9].The problems of piezoelectric cantilever beams are usually difficult to be solved analytically due to the existence of the force–electric coupling constitutive relation
The bending problem of a piezoelectric cantilever beam under combined loads is solved. It can be seen from the derivation above that the piezoelectric effect is not shown in the zero-order perturbation solution, that is, the zero-order perturbation solution is the solution of the cantilever beam without piezoelectric properties which is regarded as the unperturbed system
Summary
Piezoelectric polymers have been widely used in sensors, actuators, electronic information and intelligent structures because of its great force–electric coupling characteristics [1,2,3,4,5,6]. Shi et al [22,23] studied the analytical solution of a density functionally gradient piezoelectric cantilever under axial and transverse uniform loads and applied DC voltages and solved the force–electric coupling plane strain problem of supported beams under a uniform load by the inverse method. The application solved by using load and beam height differences as perturbation parameters Later, He and Chen of the multi-parameter perturbation method in beam problem was proposed by Chien [29] in 2002,.
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