Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermal loading based on a novel HSDT

Abstract

This paper studies the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermal loading based on a novel higher-order shear deformation theory (HSDT). Nonlocal elasticity theory is applied to consider the small-scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical method is utilized to decrease the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Then, the analytical solutions are obtained based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature-dependent. The impacts of the several variables are examined on the nonlinear frequency ratio of the nanobeams. The results illustrate that when the maximum deflection is smaller/greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.

KEYWORDS:

• Magneto-electro-thermo-elastic nanobeams
• novel HSDT
• nonlocal elasticity theory
• size effect
• perturbation technique

Acknowledgements

Scientific Research Fund of Hunan Provincial Education Department (No.15C1240) and Innovation platform open fund Project (No.16K080) and Scientific Research Fund of Hunan Provincial Education Department (NO. 20C1651).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

]