Bending and free vibration of a circular magnetoelectroelastic plate with surface effects

Abstract

Surface effects play a significant role in affecting the mechanical behavior of nanosized NEMS such as sensor, actuator, transducer. This paper studies the bending and free vibration of a magnetoelectroelastic plate with surface effects. By incorporating surface effects into the Kirchhoff theory of thin plates, the governing differential equation for bending and vibration of a magnetoelectroelastic plate is derived. Simply supported and clamped circular plates are analyzed for applied mechanical loading, electric voltage, and magnetic potential difference. An analytical method is presented to obtain closed form solutions for static deflection of bending and natural frequencies of free vibration. The well-known results of circular thin plates are recovered if ignoring the surface effects along with coupling coefficients. A comparison of the deflections and the natural frequencies with their counterparts in the absence of surface effects shows that surface residual tension plays a crucial role, which decreases the deflection and increases the natural frequencies. The influence of surface magnetoelectroelasticity is discussed and the small scale effect can be captured. The obtained results are helpful for design and application of NEMS.