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.

本文考虑了在磁和热载荷作用下粘弹性碳纳米锥（CNC）的动态屈曲。此类纳米结构在诸如扫描探针显微镜的纳米机电系统（NEMS）中具有广泛的应用。根据开尔文-沃格特的方法研究了结构阻尼的影响。假设使用粘滞-帕斯泰纳克模型，CNC周围的粘弹性介质。利用汉密尔顿原理，能量方法，一阶剪切变形理论（FSDT），确定了运动方程，其中通过高阶非局部应变梯度方法捕获了尺寸的影响。Bolotin方法和微分正交方法（DQM）用于求解运动方程，以获取动态不稳定区域（DIR）的形成。研究了边界条件，非局部参数，结构阻尼，磁场，粘弹性介质，温度变化以及CNCs半顶角等因素对DIR的影响。结果表明，随着应变梯度参数的增加，DIR将在高频下发生。此外还发现，磁负载对纳米结构的DIR具有积极影响。