Nonlinear vibration analysis of circular multilayer graphene-based NEMS sensors using harmonic balance and pseudo-arclength continuation methods

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2025-06-19 DOI:10.1016/j.ijnonlinmec.2025.105187

Milad Saadatmand, Junghwan Kook

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引用次数: 0

Abstract

In this study, the partial differential equation (PDE) for a circular multilayer graphene-based nano-electro-mechanical (NEMS) capacitive sensor was formulated in polar coordinates, considering electrostatic effects with fringing field correction, intermolecular Casimir force, and harmonic external pressure. The continuum model incorporates a nonlocal parameter based on Eringen's theory and interlayer shear effects. Using 8th order polynomial trial functions in the Galerkin reduced order method (ROM) for clamped boundary conditions, the equation for the first mode shape was derived. The natural frequencies in different graphene layers were compared with similar studies on rectangular multilayer graphene sheets (MLGSs). Voltage-frequency graphs highlighted the importance of Casimir force in small scenarios. After validating the mathematical model, nonlinear vibration analysis was performed using the harmonic balance method and pseudo-arclength continuation. The frequency-response (F–R) curves revealed softening behavior even at small deflections and superharmonic resonance under high pressures. Excellent agreement was observed between the direct numerical integration and the third order harmonic balance method. Finally, the influence of applied voltage on the nonlinear dynamics of the MLGS-based NEMS sensor was presented.

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基于谐波平衡和伪弧长延拓法的圆形多层石墨烯NEMS传感器非线性振动分析

在极坐标下，考虑带边场校正的静电效应、分子间卡西米尔力和谐波外压，建立了圆形多层石墨烯纳米机电（NEMS）电容式传感器的偏微分方程。连续介质模型结合了基于Eringen理论的非局部参数和层间剪切效应。利用箝位边界条件下伽辽金降阶法（ROM）中的8阶多项式试函数，推导了第一阶模态振型方程。将不同石墨烯层的固有频率与矩形多层石墨烯片（MLGSs）的相似研究进行了比较。电压-频率图突出了卡西米尔力在小场景中的重要性。在验证数学模型后，采用谐波平衡法和伪弧长延拓进行了非线性振动分析。频率响应曲线（F-R）显示出即使在小挠度和高压下的超谐波共振下的软化行为。结果表明，直接数值积分法与三阶谐波平衡法具有较好的一致性。最后，分析了外加电压对基于mlgs的NEMS传感器非线性动力学特性的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.