Effect of magnetic-thermal field on nonlinear wave propagation of circular nanoplates

ABSTRACT

In this article, an analytical approach is developed to investigate the nonlinear vibrational behavior of an graphene sheet. In order to be a practical instance, the circular nanoplate is also resting on an external Pasternak elastic medium including the Winkler modulus and shear modulus parameters. At the same time, it is subjected to the magnetic field and a thermal load. The modified couple stress theory as well as Eringen nonlocal elasticity theory involving small scale parameters are implemented to justify the size-dependent effects. The governing equations are derived based on von Kármán nonlinear strain–displacement relations. The presented method is verified by comparing the obtained results to their counterparts reported in the published literature. Effects of various parameters such as nonlocal parameters, temperature change, and elastic medium coefficients for different boundary conditions are also discussed. Numerical results reveal that the intrinsic size-dependent property of material increases the natural frequency.

KEYWORDS:

• Analytical approach
• nonlinear vibration
• circular graphene sheet
• magnetic field
• couple stress theory

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

E. Allahyari http://orcid.org/0000-0003-2300-5130

M. Asgari http://orcid.org/0000-0002-2063-8699

Additional information

Notes on contributors

E. Allahyari

Ehsan Allahyari is an PhD, Research Assistant at the Mechanical Engineering Department, K.N. Toosi University of Technology, Iran. He was the Top Ranked M.S. student of Mechanical Engineering Department, Qom University of Technology. His research interests are Non-linear Mechanics and Bending and Vibration Analyses of Beams, Plates, and Shells. He also has published many high quality articles about nonlinear vibration of plates with analytical approach in various journals.

M. Asgari

Masoud Asgari is an associate professor at the Mechanical Engineering Department, K.N. Toosi University of Technology, Iran. He was the Top Ranked B.S. student of Mechanical Engineering Department, Amirkabir University of Technology. He received a MSc and Ph.D in Mechanical Engineering from Amirkabir University of Technology (2003–2005) and Sharif University of Technology (2006–2010), Iran. His research interests are Thermo-mechanical Analysis of Advanced Composite Material Structures and nonlinear Vibration Analysis of Advanced Composite Material Structures.