76
G. Chakraborty and N. Jani
Fig. 7 a Utilizing jump phenomena for sensing purpose. b Tracking the bifurcation frequency in
parametrically excited systems
earities, a reduction in angle random walk (ARW) and bias instability is
possible.
(iv) Nonlinear coupling between two modes of a micromechanical resonatory
disc gyroscope introduces the parametric amplification of the Coriolis force
without the need of externally applied parametric pumping [41]. The amplification increases the rate sensitivity of vibrating gyroscope.
(v) As described in previous section, large displacement reduces the sensor
performance and detecting the displacement also becomes difficult. To limit
the displacement, nonlinearity is introduced in the excitation loop [42]. In
some of the mass-sensing strategies, microcantilever is operated in selfexcitation loop. Tip deflection of cantilever beam is detected and (as shown
in Fig. 8) base displacement is given as cubic polynomial function of the
sensor output [43]. Self-excitation strategy has also been utilized for creating
parametric resonance [15]. Here, the introduced nonlinearity will not cause
any jumps in amplitude while sweeping of the excitation frequency.
d. Memory devices
In memory elements, bistability is introduced into the system to generate two
states in the response amplitude, namely, 0 and 1 states, which correspond to
the low and high values of the amplitude, respectively. Such bistability, through
which amplitude is switched from one state to the other, is possible only because
of nonlinearities [44].
6 Tailoring Nonlinearity in MEMS Resonator
It is seen that adjustment of nonlinearity either by reducing it or enhancing may be
required in MEMS resonator. Special arrangements are made to modify the nonlinearity in the existing microstructures. Some are listed below:
G. Chakraborty and N. Jani
Fig. 7 a Utilizing jump phenomena for sensing purpose. b Tracking the bifurcation frequency in
parametrically excited systems
earities, a reduction in angle random walk (ARW) and bias instability is
possible.
(iv) Nonlinear coupling between two modes of a micromechanical resonatory
disc gyroscope introduces the parametric amplification of the Coriolis force
without the need of externally applied parametric pumping [41]. The amplification increases the rate sensitivity of vibrating gyroscope.
(v) As described in previous section, large displacement reduces the sensor
performance and detecting the displacement also becomes difficult. To limit
the displacement, nonlinearity is introduced in the excitation loop [42]. In
some of the mass-sensing strategies, microcantilever is operated in selfexcitation loop. Tip deflection of cantilever beam is detected and (as shown
in Fig. 8) base displacement is given as cubic polynomial function of the
sensor output [43]. Self-excitation strategy has also been utilized for creating
parametric resonance [15]. Here, the introduced nonlinearity will not cause
any jumps in amplitude while sweeping of the excitation frequency.
d. Memory devices
In memory elements, bistability is introduced into the system to generate two
states in the response amplitude, namely, 0 and 1 states, which correspond to
the low and high values of the amplitude, respectively. Such bistability, through
which amplitude is switched from one state to the other, is possible only because
of nonlinearities [44].
6 Tailoring Nonlinearity in MEMS Resonator
It is seen that adjustment of nonlinearity either by reducing it or enhancing may be
required in MEMS resonator. Special arrangements are made to modify the nonlinearity in the existing microstructures. Some are listed below: