In this project, an aeroelastic model for electrostatically actuated microbeams subjected to external airflow is investigated. The effect of flow velocity on the static and dynamic pull-in instability phenomena is surveyed. The airflow passes between a microbeam and a ground rigid plate. Both doubly-clamped and cantilever micro-beams are analyzed. The first-order fringing field effect is included for modeling electrostatic force. Moreover, membrane stretching of microbeam generated by immovable boundary conditions is accounted to improve accuracy. Navier-Stokes’ equation is utilized for deriving fluid-structure interaction (FSI) equation. The results indicate that contrary to the singly-clamped microbeam, by considering dynamic pressure of external flow, a doubly-clamped microbeam would become unstable sooner and pull-in instability could occur for lower voltages. However, this effect for the doubly-clamped microbeam could be ignored except for very high velocities. In addition, we could observe a significant retardation in pull-in instability for a cantilever microbeam in the range of pre-flutter velocities. By including the gyroscopic terms for this microbeam, we could see a significant rise-and-fall effect for the post-flutter and pre-flutter velocities, respectively. Moreover, in the field of nanosystems, we introduce carbon nanotubes (CNT) as a material that has a significant potential for application in the FSI fields. Therefore natural frequency and nonlinear response of CNT conveying fluid based on coupling of nonlocal theory and von Karman’s stretching are obtained. Homotopy analysis method (HAM) is used for solving nonlinear differential equation of system and convergence region of approach presented. Effects of mid-plane stretching, nonlocal parameter and their coupling in the model are investigated. It is concluded that stretching effect is significant only for higher-amplitude initial excitations and lower beam aspect ratios. Moreover, by including the slip boundary condition, the effect of nano-size flow is revealed for the nonlinear vibration model. We conclude that small-size effects of nano-tube and nano-flow have impressed critical velocity of fluid significantly, specially, for gas fluid. Analytical results obtained from HAM solution show a satisfactory agreement with numerical solutions such as Runge-Kutta. Having an analytical approach, we have been able to investigate the unbounded growth of amplitude of vibrations for flow velocities near the critical velocity. For the rest of this survey, an electromechanical model is proposed for CNTs conveying fluid and by this way, the effect of applied voltage on the natural frequencies and divergence instability is investigated. The Van der Waals force between the outer surface of nanotube and substrates is also included in the modeling. Two methods of actuation are considered for electrostatic actuation as the single-side and double side actuation. We conclude that both of these methods reduce the stability of nanotube and critical flow velocities. Therefore, a combined method is proposed as the third method of actuation by exerting some controls based on the transverse displacement and velocity of the midpoint of nanotube. The effects of considering these controls on the stability and limitation of the vibration amplitude of nanotube are revealed by determining the nonlinear dynamic response of the nanotube obtained from numerical solutions. Keyword : carbon nanotube (CNT), homotopy analysis method (HAM), slip boundary condition, fluid-structure interaction (FSI), microelectromechanical systems (MEMS), nanoelectromechanical systems (NEMS)
