Thermoelastic modeling and comparative analysis of biomass sensors under rippling deformation and magnetic field. (English) Zbl 1481.74562
Summary: 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 Kármán geometric nonlinearity. This study shows the importance of considering the nonlinear effects on the system’s sensitivity from frequency and amplitude sensing techniques.
MSC:
| 74M05 | Control, switches and devices (“smart materials”) in solid mechanics |
| 74F05 | Thermal effects in solid mechanics |
| 74F15 | Electromagnetic effects in solid mechanics |
Keywords:
carbon nanotubes mass sensing; rippling deformation; magnetic field; thermal loading; sensitivityReferences:
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