Interdisciplinary Applied Mathematics

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FIGURE 18.23. (a) Equivalent circuit element for squeezed film damping. (b) Equivalent circuit for squeezed film damping in the entire gap.

where m and n are odd integers, AWL is the plate area, and cW/L. Here W and L are the width and length of the mass planar surfaces as shown in Figure 18.22; S is the squeeze number given by

12p,eW 2

2    ^5


and ш is the angular frequency. The forces in equations (18.14), (18.15) can be represented by the electrical equivalent circuit using a combination of an inductance (equals the spring behavior of the gas) and a resistance (acts as a damping element) in series, as shown in Figure 18.23(a). Figure 18.23(a) shows a single element for a corresponding m and n. The actual equivalent circuit for squeezed film damping would consist of a parallel combination of such elements (for various m and n) connected in parallel to the MEM device circuit as shown in Figure 18.23(b). The governing differential equation for the circuit shown in Figure 18.23(a) is


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