Figure 4.The sense modes of the micromachined gyroscopes.4.?Resonant Dovitinib cancer Frequencies of the Micromachined GyroscopesThe drive modes of the introduced gyroscopes are the flexural vibrations Inhibitors,Modulators,Libraries of the slanted beams, which are normally excited by supplying a sinusoidal signal plus DC bias voltage. The equivalent kinematic models are shown in Figure 5.Figure 5.Kinematic analysis of the drive mode: flexural vibration of the slanted beam. (a) clamped-clamped (b) clamped-free.In addition, the beams follow the Euler-Bernoulli beam theory. Considering two types of gyroscopes driven by same conditions, the stiffness of the clamped-clamped beam kdC-C and the stiffness of the clamped-free beam kdC-F can be described as:kdC-C=6EIl3(2)kdC-F=3EIl3(3)where E is the Young��s modulus of silicon, I is the moment of inertia, l is the length of the suspended beam.
Because the gyroscopes are vacuum packaged, the resonant frequency ��n can be considered as the natural frequency. Thus, the resonant frequencies of drive modes can Inhibitors,Modulators,Libraries be given by:��dC-C=2��dC-F=km=6EIml3(4)From the Equation (4), we can conclude that the resonant frequency of the drive mode of the Inhibitors,Modulators,Libraries C-C beam is 2 times as high as that of the C-F beam. The sense modes of the Inhibitors,Modulators,Libraries introduced gyroscopes are the torsional vibrations of the slanted beams. The equivalent kinematic models are shown in Figure 6.Figure 6.Kinematic analysis of the sense mode: torsional vibration of the slanted beam. (a) clamped-clamped (b) clamped-free.
Similar to the drive mode Cilengitide oscillator, the stiffness of the clamped-clamped beam ksC-C and the stiffness of the clamped-free beam ksC-F can be described as:ksC-C=3GIpl(5)ksC-F=GIpl(6)where G is the shear modulus of silicon, Ip is the area moment of inertia.The resonant frequencies of sense modes for two types of gyroscopes can be given by:��sC-C=3��sC-F=3GIpJl(7)where J is the moment of inertia of the proof mass with respect to the rotatio
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