Abstract This study is intended for investigating the linear and nonlinear responses of carbon nanotube-based mass sensors in thermal and magnetic environment. For accurate modeling, the carbon nanotube rippling deformation effect is considered and various representations for the thermal expansion are examined and compared to each other. By utilizing Euler-Bernoulli beam theory assumptions and Eringen's nonlocal elasticity theory, the nonlinear reduced-order model is developed on the basis of the extended Hamilton's principle. The results show that the natural and resonant frequencies and frequency shifts of the system are strongly dependent on the magnetic field and thermal expansion representation. The method of multiple scale is used to determine the modulation equation including the von Karman and rippling nonlinearities. The results show a very good agreement between the perturbation solution and the numerical integration results for specific conditions of the forcing, temperature difference, and quality factor. A comparative study between the linear and nonlinear mass sensing approaches is performed to show their limits of applicability. It is demonstrated that the linear approach may result in erroneous detection of the deposited mass. The obtained results indicate that the longitudinal magnetic field enhances the dynamic stability of the carbon nanotube mechanical resonator in the pre-buckling oscillation regime, while the dynamic stability of the nanoscale resonator is decreased in the presence of the magnetic field for the post-buckling configuration. Also, the ripple-based nonlinearity is accompanied by an increase in the mass responsivity of the resonator. On the contrary, mass sensitivity of the carbon nanotube resonator is diminished by considering the von Karman geometric nonlinearity. This study shows the importance of considering the nonlinear effects on the system's sensitivity from frequency and amplitude sensing techniques.

中文翻译：

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波纹变形和磁场作用下生物质传感器的热弹性建模与对比分析

摘要 本研究旨在研究基于碳纳米管的质量传感器在热和磁环境中的线性和非线性响应。为了精确建模，考虑了碳纳米管波纹变形效应，并检查并比较了热膨胀的各种表示。利用Euler-Bernoulli梁理论假设和Eringen非局域弹性理论，基于扩展的Hamilton原理建立了非线性降阶模型。结果表明，系统的固有频率和谐振频率以及频移强烈依赖于磁场和热膨胀表示。多尺度方法用于确定调制方程，包括冯卡门和波纹非线性。结果表明，在特定的强迫、温差和品质因数条件下，扰动解与数值积分结果非常吻合。进行了线性和非线性质量传感方法之间的比较研究，以显示它们的适用性限制。已证明线性方法可能导致对沉积质量的错误检测。所得结果表明，纵向磁场增强了碳纳米管机械谐振器在预屈曲振荡状态下的动态稳定性，而纳米级谐振器的动态稳定性在磁场存在下降低了后屈曲配置. 此外，基于纹波的非线性伴随着谐振器质量响应度的增加。相反，考虑到冯卡门几何非线性，碳纳米管谐振器的质量灵敏度会降低。这项研究表明了考虑频率和幅度传感技术对系统灵敏度的非线性影响的重要性。