Thermal stress and magnetic effects on nonlinear vibration of nanobeams embedded in nonlinear elastic medium

Abstract

Nonlinear vibration of nanobeams embedded in the linear and nonlinear elastic materials under magnetic and temperature effects is investigated in this study. Von Karman’s strain–displacement relation is applied to a nonlocal Euler–Bernoulli beam model. Equation of motion is derived using Hamilton’s principle. Galerkin’s method is applied to decompose the nonlinear partial differential equation into a nonlinear ordinary differential equation (NODE). The NODE is solved using He’s method. The nanobeams are embedded in the Winkler, Pasternak, and nonlinear elastic media. The effects of low and high temperatures, nonlocal parameter, magnetic force, amplitude, and linear and nonlinear elastic materials are examined.

Keywords:

• Linear elastic medium
• magnetic force
• nonlinear elastic medium
• nonlinear vibration
• temperature effect

Acknowledgments

The authors are grateful to the University of Salahaddin-Erbil and Iran University of Science and Technology for supporting this work.

Disclosure statement

The authors declare that they have no competing interests.