Higher order nonlocal viscoelastic strain gradient theory for dynamic buckling analysis of carbon nanocones

Abstract

The dynamic buckling in viscoelastic carbon nanocones (CNCs) under the magnetic and thermal loads is considered in this article. This class of nano-structures has great application in nano-electro-mechanical system (NEMS) such as scanning probe microscopy. Structural damping influences are studied according to approach of Kelvin–Voigt. The viscoelastic medium around the CNC is assumed applying the model of visco-Pasternak. Utilizing the first order shear deformation theory (FSDT), Hamilton's principle, method of energy, the motion equations are determined where the influences of size are captured by higher order nonlocal strain gradient approach. Method of Bolotin and differential quadrature method (DQM) are utilized to solve the equations of motion in order to access the formation of dynamic instability region (DIR). The influences of different factors like, boundary conditions, nonlocal parameters, structural damping, magnetic field, viscoelastic medium, temperature changes along with CNCs semi vertex angle on the DIR are investigated. The outcomes show that with rising strain gradient parameter, the DIR will be occurred at high frequencies. It is furthermore found that the magnetic load has a positive influence on the DIR of the nano-structure.