Vibration Analysis of Size-Dependent Piezoelectric Nanobeam Under Magneto-Electrical Field

The damping vibration characteristics of magneto-electroviscoelastic (MEV) Nano beam resting on viscoelastic foundation based on nonlocal strain gradient elasticity theory (NSGT) is studied in this article. For this purpose, by considering the effects of Winkler-Pasternak, the viscoelastic medium consists of linear and viscous layers. With respect to the displacement field in accordance with the refined shear deformable beam theory (RSDT) and the Kelvin-Voigt viscoelastic-damping model, the governing equations of motion are obtained using Hamilton’s principle based on nonlocal strain gradient theory (NSGT). Using Fourier Series Expansion, The Galerkin’s method adopted to solving differential equations of Nano beam with both of simply supported and clamped boundary conditions. Numerical results are obtained to show the influences of nonlocal parameter, the length scale parameter, slenderness ratio and magneto-electro-mechanical loadings on the vibration behavior of Nano beam for both types of boundary conditions. It is found that by increasing the magnetic potential, the dimensionless frequency can be increased for any value of the damping coefficient and vice versa. Moreover, negative/positive magnetic potential decreases/increases the vibration frequencies of thinner Nano beam. In addition, the vibrating frequency decreases and increases with increasing nonlocal parameter and length scale parameter respectively.