Nonlocal vibration of a piezoelectric polymeric nanoplate carrying nanoparticle via Mindlin plate theory

This paper is concerned with the vibration characteristics of an embedded nanoplate-based nanoelectromechanical sensor made of polyvinylidene fluoride (PVDF) carrying a nanoparticle with different masses at any position. The nanoplate is surrounded by elastic medium which is simulated as Pasternak foundation. The PVDF nanoplate is subjected to an applied voltage in the thickness direction. In order to satisfy the Maxwell equation, electric potential distribution is assumed as a combination of a half-cosine and linear variation. Adopting the nonlocal Mindlin plate theory, the governing equations are derived based on the energy method and Hamilton's principle which are then solved by Galerkin method to obtain the natural frequency of the nanoplate. A detailed parametric study is conducted to elucidate the influences of the nonlocal parameter, external electric voltage, position and mass of nanoparticle, temperature changes and dimension of nanoplate and elastic medium. Results indicate that the frequency is increased as the nanoparticle comes closer to the center of the nanoplate; also increasing mass of the nanoparticle decreases the frequency of the system. This study might be useful for the design of PVDF nanoplate-based resonator as nanoelectromechanical sensor.