78
G. Chakraborty and N. Jani
Fig. 9 Microbeam with initially curved shape (arch beam)
Fig. 10 Modifying the cubic nonlinearity coefficient through varying the thickness
7 Conclusion
Different aspects of nonlinearities on the overall dynamics of MEMS resonators
have been reviewed. Both desirable and undesirable effects of nonlinearities are
discussed with the help of simple mathematical models. Although many facts of
nonlinearities are dealt with, an exhaustive study is impossible because, unlike linear
system, there is no general solution of nonlinear equation of motion. Consequently,
different excitations have different effects. Furthermore, only one type of system,
namely, the one which can be modelled as single-degree-of-freedom system has been
considered here. Coupled array of micromachined oscillators or the MEMS where
multiple modes interact due to nonlinearity has not been discussed. Any meaningful
discussion of the dynamic behaviour of such system will make the size of the article
too large to be within the limit.
References
1. Lavrik, N.V., Sepaniak, M.J., Datskos, P.G.: Cantilever transducers as a platform for chemical
and biological sensors. Rev. Sci. Instrum. 75(7), 2229–2253 (2004)
2. Zhao, L., Hu, Y., Wang, T., Ding, J., Liu, X., Zhao, Y., Jiang, Z.: A mems resonant sensor
to measure fluid density and viscosity under flexural and torsional vibrating modes. Sensors
16(6), 830 (2016)
3. Todaro, M.T., Guido, F., Mastronardi, V., Desmaele, D., Epifani, G., Algieri, L., De Vittorio,
M.: Piezoelectric mems vibrational energy harvesters: advances and outlook. Microelectron.
Eng. 183, 23–36 (2017)
G. Chakraborty and N. Jani
Fig. 9 Microbeam with initially curved shape (arch beam)
Fig. 10 Modifying the cubic nonlinearity coefficient through varying the thickness
7 Conclusion
Different aspects of nonlinearities on the overall dynamics of MEMS resonators
have been reviewed. Both desirable and undesirable effects of nonlinearities are
discussed with the help of simple mathematical models. Although many facts of
nonlinearities are dealt with, an exhaustive study is impossible because, unlike linear
system, there is no general solution of nonlinear equation of motion. Consequently,
different excitations have different effects. Furthermore, only one type of system,
namely, the one which can be modelled as single-degree-of-freedom system has been
considered here. Coupled array of micromachined oscillators or the MEMS where
multiple modes interact due to nonlinearity has not been discussed. Any meaningful
discussion of the dynamic behaviour of such system will make the size of the article
too large to be within the limit.
References
1. Lavrik, N.V., Sepaniak, M.J., Datskos, P.G.: Cantilever transducers as a platform for chemical
and biological sensors. Rev. Sci. Instrum. 75(7), 2229–2253 (2004)
2. Zhao, L., Hu, Y., Wang, T., Ding, J., Liu, X., Zhao, Y., Jiang, Z.: A mems resonant sensor
to measure fluid density and viscosity under flexural and torsional vibrating modes. Sensors
16(6), 830 (2016)
3. Todaro, M.T., Guido, F., Mastronardi, V., Desmaele, D., Epifani, G., Algieri, L., De Vittorio,
M.: Piezoelectric mems vibrational energy harvesters: advances and outlook. Microelectron.
Eng. 183, 23–36 (2017)