Abstract

The aims and objectives of the current study are to investigate the vibration analysis of the graphene sheet with attached spring, mass, and damper system for the first time. For this purpose, the governing equation is derived employing Hamilton’s principle regarding the nonlocal Eringen theory. The graphene sheet is supposed to be rested on a Winkler elastic foundation. Galerkin’s method is being used to obtain frequency on various boundary conditions. To validate our work, the proposed model is demonstrated by comprising the present model with the results available in the literature. The influence of different parameters such as the attached mass, nonlocal parameter, aspect ratio, and Winkler foundation of a graphene sheet on the non-dimensional vibration frequencies are presented in detail. The results indicate that adding the spring-mass system leads to an increase in the non-dimensional frequency parameter. The outcomes of this survey can be utilized in the construction of biological and chemical nanosensors.

摘要

本研究的目的和目的是首次研究附有弹簧、质量和阻尼系统的石墨烯片的振动分析。为此目的，控制方程是利用关于非局部 Eringen 理论的 Hamilton 原理推导出来的。石墨烯片应该放在温克勒弹性基础上。Galerkin 的方法被用于获得各种边界条件下的频率。为了验证我们的工作，提出的模型通过将当前模型与文献中可用的结果相结合来证明。详细介绍了石墨烯片的附着质量、非局部参数、纵横比和Winkler基础等不同参数对无量纲振动频率的影响。结果表明，添加弹簧质量系统会导致无量纲频率参数的增加。这项调查的结果可用于构建生物和化学纳米传感器。