Comments on nonlocal effects in nano-cantilever beams

In this paper, vibration characteristics of magneto-electro-thermo-elastic functionally graded (METE-FG) nanobeams is investigated in the framework of third order shear deformation theory. Magneto-electro-thermo-elastic properties of FG nanobeam are supposed to vary smoothly and continuously along the thickness based on power-law form. To capture the small size effects, Eringen’s nonlocal elasticity theory is adopted. By using the Hamilton’s principle, the nonlocal governing equations are derived and then solved analytically to obtain the natural frequencies of METE-FG nanobeams. The reliability of proposed model and analytical method in predicting natural frequencies of METE-FG nanobeam is evaluated with comparison to some cases in the literature. Numerical results are provided indicating the influences of several parameters including magnetic potential, external electric voltage, temperature fields, power-law exponent, nonlocal parameter and slenderness ratio on the frequencies of METE-FG nanobeams. It ...

Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment:

In this study, the free vibration and buckling responses of functionally graded nanoplates with magneto-electro-elastic coupling are studied for the first time using a nonlocal modified sinusoidal shear deformation plate theory including the thickness stretching effect. The constitutive relations for these kind of structures are defined. The equations of motion for rectangular sandwich plates in macro and nano scale are derived using a modified dynamic version of Hamilton's principle including a contribution of the electric and magnetic fields. The closed-form analytical solution to simply supported plates is obtained using Navier solution technique. A power-law distribution and a half cosine variation are used to model the variation of materials properties and electric/magnetic potentials, respectively. The analytical solutions are verified with well-known solutions in the literature. A parametric study was conducted to show the effect of nonlocal parameter, power-law index, predefined electric and magnetic fields, axial compressive and tensile forces, the aspect ratio of plates, and volume ratio of functionally graded and piezomagnetic layers on mechanical behaviors of nanoplates. Obtained numerical results can be used as benchmark values for validation of correctness of diverse analytical and numerical methods applied for design and analysis of composite nanoelectromechanical systems.

Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory

Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory

In this article, free vibration behavior of magneto–electro–thermo-elastic functionally graded nanobeams is investigated based on a higher order shear deformation beam theory. Four types of thermal loading including uniform and linear temperature change as well as heat conduction and sinusoidal temperature rise through the thickness are assumed. Magneto–electro–thermo-elastic properties of FG nanobeam are supposed to change continuously throughout the thickness based on power-law model. Via nonlocal elasticity theory of Eringen, the small size effects are adopted. Based upon Hamilton’s principle, the coupled nonlocal governing equations for higher order shear deformable METE-FG nanobeams are obtained and they are solved applying analytical solution. It is shown that the vibrational behavior of METE-FG nanobeams is significantly affected by various temperature rises, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio.

S.Y. Shi

Papers

Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory