Size-dependent free vibration of functionally graded magneto-electrothermo- elastic nanobeams resting on Winkler-Pasternak foundation using nonlocal elasticity theory

The main aim of this paper is to investigate the size-dependent free vibration of functionally graded magnetoelectro- thermo-elastic (METE-FG) nanobeams subjected to magnetic and electric potentials and temperature rise resting on the Winkler-Pasternak foundation based on the nonlocal elasticity theory of Eringen. In order to model thenanobeam the Euler-Bernoulli beam theory is employed. It is assumed that the material properties of nanobeam are distributed continuously through the thickness of nanobeam. Using Hamilton’s principle, the equations of motion of the magneto-electro-thermo-elastic nanobeam are derived. By employing the nonlocal elasticity theory, the small-scaleeffect is considered in modeling the mechanical behavior of nanobeams. The simply supported boundary condition is applied and the governing equations are solved using Navier’s solution. The numerical predictions are presented and discussed for BaTiO3–CoFe2O4 nanobeams. The results that are predicted by the present theory are validated bycomparing with the results available in the literature. Moreover, the effects of different parameters such as spring and shear foundation parameters, external magnetic potential, external electric voltage, temperature rise, power-law index and nonlocal parameter on the natural frequency of functionally graded magneto-electro-thermo-elastic nanobeam are studied.

کلیدواژه ها:

Magneto-electro-elastic nanobeam ، functionally graded material ، nonloal elasticity theory ، free vibration ، Winkler-Pasternak foundation.