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Damping in a vibratory mechanical device plays an important role in modulating the response of the system. It is of critical importance to understand the nature of damping and to be able to effectively control it for micro-machined devices such as sensors or actuators. For example, if damping is too low in a micro-machined lateral accelerometer, the severe degree of resonance of the accelerometer upon an impact of external force may produce such a large signal that cripples its control circuitry resulting in total system failure. High damping (near critical) is generally desired for accelerometers. As for yaw rate gyroscopic sensors, on the other hand, low damping is required in order to achieve sufficient sensitivity of the system under a given driving force and for certain types of applications. Therefore, in designing a MEMS device, the consideration of damping must be taken into account at the earliest stage. Micro-Electro-Mechanical-System (MEMS) devices are often operated in an isolated environment filled with nitrogen or other types of gas such that the gas functions as a working fluid and dissipates energy. A gas film between two closely spaced parallel plates oscillating in normal relative motion generates a force, due to compression and internal friction, which opposes the motion of the plates. The damping, related to energy loss of the system, due to such a force is referred to as squeeze film damping. In other cases, two closely spaced parallel plates oscillate in a direction parallel to each other, and the damping generated by a gas film in this situation is referred to as shear damping. Under the small motion assumption, both flow induced force is linearly proportional to the displacement and velocity of the moving plates. The coefficient of the velocity is the damping coefficient. The review will start with a discussion on effective viscosity coefficients that were used in some of the early work by T. Veijola et al., M. Andrews et al. and others. In general, the capping pressure for a micro-machined system is below or much below the atmospheric pressure. As pressure decreases, the mean free path of the gas molecules ( nitrogen for example) increases. When the mean free path is comparable to the air gap between two plates, one may no longer be able to treat the gas as continuum. Therefore, an effective viscosity coefficient is introduced such that governing equations of motion for fluid at relatively high pressures can still be used to treat fluid motion at low pressures where the mean free path is comparable or even larger than the air gap of the plates
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