Abstract
In this study, a multi-parameter perturbation method is used for the solution of a functionally-graded, thin, circular piezoelectric plate. First, by assuming that elastic, piezoelectric, and dielectric coefficients of the functionally-graded materials vary in the form of the same exponential function, the basic equation expressed in terms of two stress functions and one electrical potential function are established in cylindrical coordinate system. Three piezoelectric coefficients are selected as perturbation parameters, and the established equations are solved by the multi-parameter perturbation method, thus obtaining up to first-order perturbation solutions. The validity of the perturbation solution obtained is verified by numerical simulations, based on layer-wise theory. The perturbation process indicates that adopting three piezoelectric coefficients as perturbation parameters follows the basic idea of perturbation theory—i.e., if the piezoelectricity may be regarded as a kind of introduced disturbance, the zero-order solution of the disturbance system corresponds exactly to the solution of functionally-graded plates without piezoelectricity. The result also indicates that the deformation magnitude of piezoelectric plates is smaller than that of plates without piezoelectricity, due to the well-known piezoelectric stiffening effect.
Highlights
Piezoelectric materials have electromechanical coupling characteristics—i.e., they may generate mechanical deformation in an electric field and at the same time, electrical polarization under mechanical loads
After the validity of the multi-parameter perturbation solution is verified by numerical simulation, the perturbation solution may be used to discuss some interesting topics, including the effect of the functional gradient index on the solution, as well as the deflection difference between functionally-graded piezoelectric materials (FGPMs) plates and FGM plates
Adopting the three piezoelectric coefficients as perturbation parameters follows the basic idea of perturbation theory—i.e., if pure FGM plates without piezoelectric effects are taken as the undisturbed system, and the piezoelectric effect may be introduced as a kind of disturbance
Summary
Piezoelectric materials have electromechanical coupling characteristics—i.e., they may generate mechanical deformation in an electric field and at the same time, electrical polarization under mechanical loads. This important characteristic makes them a good candidate for a variety of electromechanical devices—for example, sensors and actuators used extensively in electromechanical conversion [1,2,3,4]. Piezoelectric sensors are usually a laminated original made by ceramic slice For this kind of laminated original, it is easy to cause stress concentration and promote the growth of interfacial microcracks, which further limits the application and development of the piezoelectric original. Since there is no obvious interface in this kind of material, the damage caused by the stress concentration at the interface can be avoided
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