Eshelby-Mori-Tanaka and the Extended Mixture Rule Approaches for Nonlocal Vibration of Piezoelectric Nanocomposite Plate with Considering Surface Stress and Magnetic Field Effects

In this research, the surface stress effect on the nonlocal vibration of piezoelectric square plate reinforced by single walled carbon nanotubes (SWCNTs) based on classical plate theory (CPT) and first order shear deformation theory (FSDT) is presented. The elastic properties of piezoelectric nanocomposite plate are estimated by Eshelby-Mori-Tanaka and the extended mixture rule approaches. The motion equations of nanocomposite plate are obtained using Hamiton's principle. The Navier's type solution is used to solve these equations. There is the best agreement between the obtained analytical results and other literature results. Then the effects of various parameters such as elastic foundation, surface stress, agglomeration, applied voltage and magnetic field on the nonlocal natural frequency of piezoelectric square nanocomposite plate are investigated. It is concluded that the non-dimensional frequency ratio decreases with increasing the SWCNT volume fraction in the inclusion (agglomeration effect), nonlocal parameter and residual surface stress constant for both CPT and FSDT. Also it is seen that a change in the applied voltage, magnetic field intensity, elastic foundation parameters and surface density leads to increase the non-dimensional frequency ratio.