On the stability of a microbeam conveying fluid considering modified couple stress theory
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On the stability of a microbeam conveying fluid considering modified couple stress theory Sonia Ahangar • Ghader Rezazadeh • Rasool Shabani • Goodarz Ahmadi • Alireza Toloei
Received: 1 June 2011 / Accepted: 16 September 2011 / Published online: 27 September 2011 Ó Springer Science+Business Media, B.V. 2011
Abstract In this paper, the size-dependent vibrational behavior of a microbeam conveying fluid was investigated using the Modified Couple Stress Theory. For cantilever and clamped-clamped microbeams, the small amplitude vibration equation of the microbeams was solved using a Galerkin based reduced order model and the effects of material length-scale parameter on its natural frequencies were evaluated. It was found that for the both cantilever and clampedclamped conditions, the critical fluid velocities predicted by the modified couple stress theory are higher than those predicted by the classical beam theory. In addition, the differences between the
S. Ahangar G. Rezazadeh (&) R. Shabani Mechanical Engineering Department, Urmia University, Urmia, Iran e-mail: [email protected] S. Ahangar e-mail: [email protected] R. Shabani e-mail: [email protected] G. Ahmadi Mechanical & Aeronautical Engineering Faculty, Clarkson University, Potsdam, NY 13699-5725, USA e-mail: [email protected] A. Toloei Aerospace Engineering Department, Faculty of New Technology and Energy Engineering, Shahid Beheshti, Tehran, Iran e-mail: [email protected]
eigen-frequencies and the critical fluid velocities predicted by the modified couple stress theory and classical beam theory depends on the ratio of the material length-scale parameter to the beam height. In addition an unexpected result in the difference between the first eigen-frequency of the cantilever micro-beam obtained by the classical and the modified couple stress theory has been achieved. Keywords MEMS Microbeam conveying fluid Size effect Couple stress theory
1 Introduction The trends of miniaturization in engineering, such as micro-electro-mechanical systems (MEMS), electronic materials, ultra-thin films, etc., require a comprehensive understanding of the effect of intrinsic micro-structure on material’s macroscopic response. Recent experiments (Fleck et al. 1994; Stlken and Evans 1998; Molotnikov et al. 2008) have shown that materials will display strong size effect when the size of non-uniform plastic deformation field associated their characteristic length scale is on the order of microns. The conventional continuum mechanics cannot predict such size-dependent phenomena, because their constitutive models possess no material characteristic length parameters. In order to explain
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such phenomena, Ahmadi and Farshad (1973) and Ahmadi (1975, 1977) obtained the equation of nonlocal elasticity over the thickness of a thin plate and also studied the theory of nonlocal viscoelastic media, which the constitutive equation of strain and strain rate dependent, stress and stress rate dependent as well as continuous memory dependent are discussed a
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