Stability Analysis of CNT Based Nano-Actuator Under Magnetic Field and Rippling Deformation

Abstract

Objective The widespread use of carbon nanotube-fabricated electromechanical systems has resulted in new operating scenarios for these structures, such as the presence of an external magnetic field. Also, rippling can significantly impact the performance of carbon nanotube-based actuators. These critical phenomena, however, are frequently overlooked in theoretical beam models. This paper simulates the electromagnetic instability of a carbon nano-tube-made actuator subjected to an external magnetic field. As the rippling bending may affect the stability performances of the nano-actuator, the influence of the rippling phenomenon is considered in the governing equation. Also, the impact of van der Waals force is incorporated in the simulation. Methods The governing equation of carbon nano-tube-manufactured nano-actuator is developed in terms of bending moment and lateral forces. Rippling is a wavelike deflection of bent carbon nanotubes on their inner arc. This configuration is crucial for large deformations, both globally and locally. The classical linear relationship between the bending and curvature cannot be employed for rippled CNT. Therefore, a modified non-linear curvature-moment relationship is used in the developed model. The impacts of the magnetic field, electrical force and van der Waals attraction are incorporated as lateral loads. The induced transverse load on the carbon nanotube due to a constant longitudinal magnetic field is simulated by using the Maxwell electrodynamics equations. Finally, the constitute equation of the nano-actuator is obtained which is a non-linear ordinary differential equation. A semi-analytical solution based on the Galerkin method is presented to solve the system’s non-linear governing equation. Results The proposed model is confirmed by comparing the resulting result to experimental data. Then, the influences of van der Waals interaction, the longitudinal magnetic flux, and rippling bending on the electromagnetic instability parameters of the nano-actuator are studied. The obtained results demonstrate that reveals that the van der Waals force reduces the instability deflection. Moreover, imposing an external magnetic field decreases the instability voltage of the system. Similarly, the instability voltage of the nano-actuator lessens by considering the rippling effect. Conclusion A mathematical model is established to study the instability of a CNT-made actuator in a magnetic environment. The model accounts for the longitudinally magnetic field using suitable body forces and the van der Waals interactions. The proposed model also takes into account the influence of rippling bending. The obtained results demonstrated that both magnetic flux and rippling phenomena reduce the instability voltage of the nano-actuator.