Dynamical characteristics of an electrically actuated microbeam under the effects of squeeze-film and thermoelastic damping P. Belardinelli a,⇑ , M. Brocchini a , L. Demeio b , S. Lenci a a DICEA, Polytechnic University of Marche, 60131 Ancona, Italy b DIISM, Polytechnic University of Marche, 60131 Ancona, Italy article info Article history: Available online 19 April 2013 Keywords: MEMS Microbeams Squeeze-film damping Thermoelastic damping Multiphysics abstract The static and dynamic behavior of a MEMS subjected to thermoelastic and squeeze-film effects is investigated. We analyse the various engineering aspects which interact in a slen- der fixed–fixed microbeam; major attention is devoted to the modeling of such a multi- physics system, including the mechanical, electrical, thermoelastic and fluid-dynamic properties with their couplings. The static solution is obtained numerically by a finite-dif- ference technique. The variation of the static deflection with respect to the voltage incre- ment, in the presence of geometric nonlinearites, is studied first. Numerical results on the magnitude of thermoelastic damping (TED) and squeeze-film damping are obtained and examined with a parametric analysis. The effect of different relaxation times imposed on the TED, both in pull-in and non pull-in regime, is studied. The squeeze-film damping is modeled by means of the Reynolds equation and the large pressure regime is investigated. We then present a comparison between the different sources of damping, evaluating their relative contribution to the system. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The ever increasing interest in Micro- and Nano-Electrical–Mechanical-Systems (commonly known as MEMS and NEMS, respectively) has recently funnelled much research work (Younis, 2011) in the linear and nonlinear dynamics of this class of dynamical systems. Their practical importance arises from a variety of applications in forefront areas of research and devel- opment, where the use of MEMS enables very smart solutions, impossible with other technologies. Some examples of MEMS are accelerometers (Luo, Zhang, Carley, & Fedder, 2002), inertial sensors (Yazdi, Ayazi, & Najafi, 1998), chemical sensors (Weinberg, Cunningham, & Clapp, 2000), filters and oscillators (Clark & Nguyen, 1995). The theoretical interest of these dynamical systems lies both in the modeling (Abdel Rahman, Younis, & Nayfeh, 2002; Fargas Marques, Costa Castello, & Shkel, 2005; Ruzziconi, Younis, & Lenci, 2013; Younis, Abdel-Rahman, & Nayfeh, 2003) and in the analysis of the response (Younis & Nayfeh, 2003). In the latter, the goal is often that of: (1) accurately determining (Rhoads, Shaw, & Turner, 2010; Roche, Cretu, & Wolffenbuttel, 2004) and controlling (Lenci & Rega, 2006) the static and dynamic pull-in threshold, which may or may not be an undesired phenomenon, depending on the application at hand, and (2) fully understanding the overall dynamical behavior in order to improve the performances of the system (Rhoads et al., 2006). Typical MEMS structures, used, for example, in resonant high sensitive sensors (Li, Tang, & Roukes, 2007; Legtenberg & Tilmans, 1994), are silicon-based slender beams with characteristic lengths in the order of microns. The mechanical model- 0020-7225/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijengsci.2013.03.011 ⇑ Corresponding author. Tel.: +39 071 2204552. E-mail addresses: p.belardinelli@univpm.it (P. Belardinelli), m.brocchini@univpm.it (M. Brocchini), l.demeio@univpm.it (L. Demeio), s.lenci@univpm.it (S. Lenci). International Journal of Engineering Science 69 (2013) 16–32 Contents lists available at SciVerse ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci