Interdisciplinary Applied Mathematics

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Does the finite width (W) of the device make the flowrate behave more like a duct flow than a channel flow?

6.1.2 Squeezed Film Effects in Accelerometers


Squeezed gas film effects in microaccelerometers have been studied by various researchers (van Kampen, 1995; da Silva et al., 1999; Veijola, 1999; Chen and Kuo, 2003). In a series of papers, Veijola et al. employed the generalized Reynolds equation to study rarefaction effects on the dynamic response of microaccelerometers (Veijola et al., 1995a; Veijola et al., 1995b; Veijola et al., 1998). A lumped parameterization of the micromechanical accelerometer shown in Figure 6.7 leads to the mass-spring-damper system represented    in    the    following    form    (see    also    Chapter    17    and    Section


18.2):


Fext:


where M is the mass, к and 7 are the spring and damping coefficients, x is the displacement of the mass, and t is time. The driving force Fext includes the applied acceleration, electrostatic, and gas damping force effects. The electrostatic force depends on the proximity between the seismic mass and the substrate (h), and it is determined by


_ eA(AV)2 e 2 h?


where e is    the    dielectric    constant    of    the    gas, A is the    plate    area, and    AV


is the electric potential difference between the moving mass and the fixed electrode. (A similar expression was used for the force in comb-drives, see Section 1.1.) The gas damping forces are obtained using the linearized Reynolds equation assuming small normal motion, small pressure variations, and also isothermal conditions under various reference pressures (Veijola et al., 1995a). The linearized Reynolds equation for oscillatory normal motion of the micromechanical accelerometer shown in Figure 6.7 is (Veijola et al., 1995a)

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