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We present a comprehensive analytical model of squeeze-film damping in perforated 3D microelectromechanical system structures. The model includes effects of compressibility, inertia, and rarefaction in the flow between two parallel plates forming the squeeze region, as well as the flow through perforations. The two flows are coupled through a nontrivial frequency-dependent pressure boundary condition at the flow entry in the hole. This intermediate pressure is obtained by solving the fluid flow equations in the two regions using the frequency-dependent fluid velocity as the input velocity for the hole. The governing equations are derived by considering an approximate circular pressure cell around a hole, which is representative of the spatially invariant pressure pattern over the interior of the flow domain. A modified Reynolds equation that includes the unsteady inertial term is derived from the Navier-Stokes …