Models for analyzing squeeze film air damping depending on oscillation modes of micro/nano beam resonators
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O R I G I NA L
Dang Van Hieu · Le Van Tam · Kazuhiro Hane · Chu Manh Hoang
Models for analyzing squeeze film air damping depending on oscillation modes of micro/nano beam resonators
Received: 18 May 2020 / Accepted: 31 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Models for analyzing squeeze film air damping depending on the oscillation mode of cantilever and double-clamped micro/nanobeam resonators are presented. The models are obtained from the damping theory of a rigid rectangular plate moving parallelly to a nearby object in viscous and molecular flow regime and electrostatic theory. The analysis results based on the models show that the influence of oscillation mode on squeeze film air damping in viscous regime is remarkably large compared to that in molecular flow regime. The damping in the first-order mode is larger than that in the high-order modes, while there is little deference in damping among the high-order modes. The damping of oscillation modes depends strongly on the oscillation amplitude and electrostatic spring softening. The obtained damping analysis models are useful for the optimal design of micro/nanobeam resonators and verifying the discrepancy between the theoretically calculated results and experiment data. Keywords Micro/nanobeam resonator · Squeeze film air damping · Oscillation mode · Electrostatic spring softening 1 Introduction Micro/nanobeam resonators are interested for a variety of applications such as RF filters, sensors, optomechanical resonators, mechanical memories, and physical measurements [1–11]. Air damping is considered as an energy loss source that strongly influences on the dynamic performance of micro/nanobeam resonators. Micro/nanobeam resonators with low air damping are required to achieve high sensitivity, low noise and low consumption energy. When a micro/nanobeam oscillates nearby an object in air or liquid environment, squeeze film air damping is often dominant compared to other damping mechanisms [12–15]. Therefore, the appropriately accurate evaluation of squeeze film air damping is important for the design of micro/nanobeam resonators. Several models for squeeze film air damping at different flow regimes have been reported [14–21]. In these models, it is assumed that the oscillation beam is a rigid body vibrating parallelly to a nearby object. However, for micro/nanobeam resonators, the beams are often operated in flexural modes. The oscillation of micro/nanobeams is nonuniform that depends on mode shapes. Recently, the operation in ambient air/fluid D. Van Hieu · L. Van Tam · C. M. Hoang (B) International Training Institute for Materials Science, Hanoi University of Science and Technology, No. 1, Dai Co Viet, Hai Ba Trung, Hanoi, Viet Nam E-mail: [email protected]; [email protected] D. Van Hieu Department of Information Technology Specialization, FPT University, Hanoi, Vietnam K. Hane Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan
D. V. Hieu et al.
Fig. 1 Schematic of a beam vibratin
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