Numerical and experimental comparison of MEMS suspended plates dynamic behaviour under squeeze film damping effect Aurelio Soma ` Æ Giorgio De Pasquale Received: 10 June 2007 / Revised: 22 February 2008 / Accepted: 29 February 2008 / Published online: 25 March 2008 Ó Springer Science+Business Media, LLC 2008 Abstract Dynamic behaviour of oscillating perforated microplates under the effect of squeeze film damping is analyzed. Two simplified finite element numerical approaches are adopted to predict damping and stiffness effects transferred from the surrounding ambient air to oscillating structures; the effects of holes cross section and plate dimension are observed. The applicability of the numerical models in terms of precision of results and mesh density is investigated. Results obtained by FE models are compared with experimental measurements conduced by an optical interferometric microscope. Keywords MEMS  Resonator  Finite element  Optical interferometry  Dynamic  Damping 1 Introduction Micro electro mechanical systems (MEMS), characterized by many different features and shapes, are currently real- ized by numerous oscillating elements and components that usually represent the upper part of a variable capacitor. Although structural parts deeply differ among applications, oscillating elements derived from the classical beam or plate shape is largely widespread. The investigation of interactions between suspended plates and surrounding gas during the oscillation is important to predict their operating behaviour. The dynamics of such a systems is not strongly influenced by inertial forces because of the smallness of structural mass, but it is strictly dependent from damping and stiffness forces generated by the air present in the thin gap separating the movable structure and substrate; the order of magnitude of this contributions, identified by the name of squeeze film damping, are frequently higher than internal damping and stiffness ones. 1.1 Literature review Many investigations have been recently realized on the squeeze film damping effect; Veijola et al. [1] proposed a compact model to consider the border flow at structure edges by extending surface dimensions and producing an equivalent damping effect. The model is referred to micro- dampers with gap size comparable to surface dimensions. Main limitation is the assumption of an incompressible flow that restricts analysis validity to low frequencies. Hutcherson and Wenjing [2] examined mechanical reso- nators behaviour at very low pressures and free-molecule regime conditions; they developed a dynamic simulation code for quality factor prediction, which results are in good agreement with experimental data. They observed that quality factor depends linearly on frequency and strongly depends on the amplitude when it is large (comparable to the gap) and is independent from amplitude when it is small. The model only considers elastic collisions between molecules and structure. Veijola [3] studied the effect of gas inertia in a squeezed- film damper both analytically and numerically, observing that this property can not be neglected above the cut-off frequency. He derived equivalent-circuit mechani- cal impedance and admittance to solve linearized Reynolds equation in continuum flow, with a small velocity and by neglecting border effects. Another analytical model [4] is A. Soma `(&)  G. De Pasquale Department of Mechanics, Polytechnic of Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy e-mail: aurelio.soma@polito.it G. De Pasquale e-mail: giorgio.depasquale@polito.it 123 Analog Integr Circ Sig Process (2008) 57:213–224 DOI 10.1007/s10470-008-9165-x