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Studying thin film damping in a micro-beam resonator based on non-classical theories

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Abstract

In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamped micro-beam bound between two fixed layers. The micro-gap between the micro-beam and fixed layers is filled with air. As classical theories are not properly capable of predicting the size dependence behaviors of the micro-beam, and also behavior of micro-scale fluid media, hence in the presented model, equation of motion governing longitudinal displacement of the micro-beam has been extracted based on non-local elasticity theory. Furthermore, the fluid field has been modeled based on micro-polar theory. These coupled equations have been simplified using Newton-Laplace and continuity equations. After transforming to non-dimensional form and linearizing, the equations have been discretized and solved simultaneously using a Galerkin-based reduced order model. Considering slip boundary conditions and applying a complex frequency approach, the equivalent damping ratio and quality factor of the micro-beam resonator have been obtained. The obtained values for the quality factor have been compared to those based on classical theories. We have shown that applying non-classical theories underestimate the values of the quality factor obtained based on classical theories. The effects of geometrical parameters of the micro-beam and micro-scale fluid field on the quality factor of the resonator have also been investigated.

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Authors and Affiliations

  1. Mechanical Engineering Department, Sahand University of Technology, Tabriz, Iran

    Mina Ghanbari & Siamak Hossainpour

  2. Mechanical Engineering Department, Faculty of Engineering, Urmia University, Urmia, Iran

    Ghader Rezazadeh

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  1. Mina Ghanbari
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  2. Siamak Hossainpour
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  3. Ghader Rezazadeh
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Correspondence to Siamak Hossainpour.

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Ghanbari, M., Hossainpour, S. & Rezazadeh, G. Studying thin film damping in a micro-beam resonator based on non-classical theories. Acta Mech. Sin. 32, 369–379 (2016). https://doi.org/10.1007/s10409-015-0482-x

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