Abstract

Motivated by the lack of sufficient accuracy in the nonlinear dynamics of the pre-stressed nano electromechanical resonators, in the present article, the concept of the dynamic instability in the pre-stressed nanoelectromechanical resonators comprehensively is investigated while the emphasis is placed on investigating the effect of the applied electric voltage. A class of nonlinear the Mathieu–Hill equation is established to determine the bifurcations while an axial parametric load is applied to excite the system. The results emphasize that the existence of different stable states allows to occur the saddle node, the supercritical, and subcritical pitchfork bifurcations.

• Highlights

• The present article provides an example of discontinuous bifurcations in a nano electromechanical system.

• The present study shows that a discontinuous bifurcation is always accompanied by a jump.

• The bifurcations classified in the present problem are considered as discontinuous ones.

摘要

由于预应力纳米机电谐振器的非线性动力学缺乏足够的精度，本文全面研究了预应力纳米机电谐振器的动态不稳定性概念，同时重点研究了影响。施加的电压。建立了一类非线性 Mathieu-Hill 方程来确定分岔，同时施加轴向参数载荷来激励系统。结果强调，不同稳定状态的存在允许发生鞍节点、超临界和亚临界干草叉分叉。

• 强调

• 本文提供了纳米机电系统中不连续分叉的示例。

• 本研究表明，不连续的分叉总是伴随着跳跃。

• 在当前问题中分类的分岔被认为是不连续的。