Nonlocal Timoshenko modeling effectiveness for carbon nanotube-based mass sensors

• Published in: European journal of mechanics, A, Solids Vol. 92; p. 104462
• Main Authors: Ceballes, S., Saunders, B.E., Abdelkefi, A.
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Masson SAS 01.03.2022; Elsevier BV
• Subjects: Beam theory (structures); Boundary conditions; Carbon; Carbon nanotube; Carbon nanotubes; Electrical properties; Equations of motion; Eringen's nonlocal elasticity; Euler-Bernoulli beam theory; Frequency shift; Hamilton's principle; Mass sensing; Mathematical models; Modelling; Nanoparticles; Nanotechnology; Nonlocal elasticity; Parameters; Particle mass; Reduced order models; Rotary inertia; Sensors; Timoshenko beam theory; Timoshenko beams; Carbon nanotube; Euler-Bernoulli beam theory; Eringen's nonlocal elasticity; Timoshenko beam theory; Mass sensing
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2021.104462

Carbon nanotubes (CNTs) have been considered for a wide range of nanotechnology applications due to their unique mechanical, thermal, and electrical properties. One of the most notable nanotechnology applications is the frequency shift-based carbon nanotube mass sensor, which has motivated the development of reliable reduced-order models. As such, this research effort focuses on a carbon nanotube-based mass sensor that utilizes Timoshenko beam theory to extend the usability of these models to short and stout structures. Additionally, Eringen's nonlocal elasticity is considered to account for certain nanoscale phenomena. To the authors' knowledge, this is the first time a CNT-based mass sensor modeled with the nonlocal Timoshenko beam theory with a complex-shaped deposited particle has been studied. Considering Timoshenko beam theory and Eringen's nonlocal theory, the Hamilton's principle is utilized to derive the governing equations of motion, boundary conditions, and continuity conditions accounting for a single deposited nanoparticle. Then, it is shown that the obtained frequency shift of the sensor is dependent on the rotary inertia, shear effects, nonlocal parameter, and particle mass, geometry, and location. The variation of each of these parameters leads to a holistic characterization of the proposed system. The discrepancies and limits of applicability between Timoshenko and Euler-Bernoulli models are deeply explored and discussed, particularly for short and stout structures. It is shown that the Euler-Bernoulli model leads to an overprediction of the frequency shifts compared to Timoshenko beam theory, especially for higher modes. The nonlocal Timoshenko-based model is valuable because short and stout structures were found to be preferred for mass sensing applications, since they lead to a higher sensitivity. Other researchers can utilize these findings for the design, modeling, and analysis of nanoscale sensors and resonators. •Nonlocal Timoshenko beam theory is developed to CNT-based mass sensors.•Eringen's nonlocal elasticity is considered to account for nanoscale phenomena.•Complex-shaped deposited particle in various locations is considered.•Sensor sensitivity is dependent on various parameters such as shear effects.•Discrepancies between Timoshenko and Euler-Bernoulli models are explored.