Magneto-Thermo mechanical vibration analysis of FG nanoplate embedded on Visco Pasternak foundation

Article history: Received: 12 July 2018 Accepted: 1 September 2018 Available online In this paper, the mechanical vibration analysis of functionally graded (FG) nanoplate embedded in visco Pasternak foundation incorporating magnet and thermal effects is investigated. It is supposed that a uniform radial magnetic field acts on the top surface of the plate and the magnetic permeability coefficient of the plate along its thickness are assumed to vary according to the volume distribution function. The effect of in-plane pre-load, viscoelastic foundation, magnetic field and temperature change is studied on the vibration frequencies of functionally graded annular and circular nanoplate. Two different size dependent theories also are employed to obtain the vibration frequencies of the FG circular and annular nanoplate. It is assumed that a power-law model is adopted to describe the variation of functionally graded (FG) material properties. The FG circular and annular nanoplate is coupled by an enclosing viscoelastic medium which is simulated as a visco Pasternak foundation. The governing equation is derived for FG circular and annular nanoplate using the modified strain gradient theory (MSGT) and the modified couple stress theory (MCST). The differential quadrature method (DQM) and the Galerkin method (GM) are utilized to solve the governing equation to obtain the frequency vibration of FG circular and annular nanoplate. Subsequently, the results are compared with valid results reported in the literature. The effects of the size dependent, the in-plane pre-load, the temperature change, the magnetic field, the power index parameter, the elastic medium and the boundary conditions on the natural frequencies are scrutinized. According to the results, the application of radial magnetic field to the top surface of plate gives rise to change the state of stresses in both tangential and radial direction as well as the natural frequency. Also, The temperature changes play significant role in the mechanical analysis of FG annular and circular nanoplate. This study can be useful to product the sensors and devices at the nanoscale with considering the thermally and magnetically vibration properties of the nanoplate.