Interdisciplinary Applied Mathematics

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This behavior is shown in Figure 6.8 for three different reference pressure conditions. The maximum amplitude of the system is a strong function of the base pressure, especially for high frequency excitations. The maximum amplitude of the frequency response of the system increases with the increased base pressure, and the shift in the phase of the system shows transition from mostly dissipative gas film behavior toward the springlike gas response. The cut-off frequency is defined as the frequency at which the dissipative and spring effects of gas are equal to each other. Figure 6.9 shows the transient time-domain response of the system to a step acceleration of 0.5 g applied for 0.5 ms under various pressures. The response of the system at 30 Pa shows slowly damped oscillations at the resonance frequency. However, higher pressure of 300 Pa eliminates these oscillations, and the mass reaches its final position within 3 ms. The distinction between these two cases is a good indication of gas damping effects as a function of the base pressure (for fixed geometry). Of course, these results can also be represented as a function of the reference Knudsen number. Using the reference gap size between the seismic mass and the substrate as 3.95 pm, we find the reference Knudsen numbers in these simulations to be Kn = 60, 6,

Accelerometer AC analysis

APLAC 6.21 User: HUT Circuit Theory Lab. Oct 25 1994

FIGURE 6.8. Simulated accelerometer amplitude and phase responses at different pressures. (Courtesy of T. Veijola.)

and 0.6 for P = 30, 300, and 3000 Pa, respectively. Therefore, Figures 6.8 and 6.9 both show the rarefaction effects on gas film damping. These results qualitatively agree with the time response of the DMD given in Figure 6.2.

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