Out-of-plane vibration of an electrostatically actuated microbeam immersed in flowing fluid
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ORIGINAL PAPER
Out-of-plane vibration of an electrostatically actuated microbeam immersed in flowing fluid Mousa Rezaee
. Naser Sharafkhani
Received: 26 October 2019 / Accepted: 4 August 2020 Springer Nature B.V. 2020
Abstract The present work investigates the out-ofplane nonlinear vibration of an electrostatically actuated cylindrical microbeam immersed in flowing fluid. The lift and drag forces as the two basic flow-induced factors affecting the dynamics of the microbeam are modeled using Van der Pol equation. The Euler– Bernoulli beam theory is used to simulate the new nonlinear model of beam cross fluid and inline motion with considering geometrical nonlinearities effects. The coupled nonlinear equations governing the microbeam out-of-plane motion and the wake oscillation are solved using the Galerkin and the step-bystep linearization methods to evaluate the response of the coupled structure to a combined applied voltage and fluid flow. Response of the microbeam to different input voltages in the presence of fluid flow is investigated in two directions of normal and parallel to fluid flow. It is shown that applying voltage not only can be used to control the lock-in regime, but also can increase the maximum dynamic amplitude up to 100 percent for a given flowing fluid. Moreover, ignoring inline vibration and geometrical nonlinearities effects may decrease the accuracy of the obtained maximum amplitude up to 18 percent in the lock-in regime.
M. Rezaee (&) N. Sharafkhani Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran e-mail: [email protected]
Keywords Out-of-plane microbeam vibration Geometrical nonlinearity Vortex-induced vibration Electrostatic force Cross fluid vibration Lock-in phenomenon
1 Introduction Electrostatic force for the first time has been used by an American physicist in generator designing and today is highly used as an actuating force in different micro-electromechanical systems due to its simple mechanism, high efficiency, reliability and less energy consumption [1, 2]. Over the past years, microbeam under the electrostatic force, as one of the most important components in different microstructures, has attracted a lot of research interests. Younis et al. [3] presented a reduced-order model to study the behavior of microbeam subjected to electrostatic force. In this model using the Galerkin method, the system converted to multi-degree of freedom model and the effects of large deflection on the behavior and stability of microbeam were studied using perturbation methods. Kuang and Chen [4] used the Adomian decomposition method (ADM) [5, 6] to solve the nonlinear equation of motion and study the unstable pull-in behavior of different types of electrostatic microactuators. Moradweysi et al. [7] investigated the pull-
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M. Rezaee, N. Sharafkhani
in instability of clamped–clamped nano-switches subjected to electrostatic and intermolecular forces. Based on the modified Adomian decomposition method,
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