A numerical method for magneto-hygro-thermal dynamic stability analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions

Abstract

Abstract The objective of this novel research is assessment of dynamic stability of a viscoelastic defective single layered graphene sheet (SLGS). Further, various kinds of defects including single vacancy (SV), double vacancy (DV) and Stone-Wales (SW) are regarded and the effects of vacancy defect reconstruction is studied as well. So as to assume this nanostructure much more realistic, Kelvin model is utilized and it is rested upon elastic foundation. This SLGS is under hygrothermal loads and in-plane magnetic forces. In addition to sinusoidal higher order shear deformation theory for modeling this nanostructure mathematically, Hamilton s principle is utilized to obtain the motion equations and furthermore nonlocal strain gradient theory (SGT) is used which considers size effects accurately. Differential quadrature method (DQM) as well as transformed weighing (TW) will be handled to solve the governing equations and determine the dynamic stability region for this nanostructure. Moreover, various moving boundary edges are studied because of hygrothermal loads. Various parameters focusing on hygrothermal loads, magnetic forces, defect kinds, defect degree, various SLGS, boundary edges and coefficients of elastic foundation and their effects upon the dynamic stability behavior of nanostructure will be investigated. In order to assess the validity, the results are compared with other papers. Based on the results, rise of defect degree causes shift of stability region to the less excitation frequencies.