80
G. Chakraborty and N. Jani
27. Antonio, D., Zanette, D.H., López, D.: Frequency stabilization in nonlinear micromechanical
oscillators. Nat. Commun. 3, 806 (2012)
28. Kaajakari, V., Mattila, T., Oja, A., Seppa, H.: Nonlinear limits for single-crystal silicon
microresonators. J. Microelectromech. Syst. 13(5), 715–724 (2004)
29. Lee, S., Nguyen, C.T.-C.: Phase noise amplitude dependence in self limiting wine-glass disk
oscillators. In: Solid State Sensor, Actuator, and Microsystems Workshop (2004)
30. Yie, Z., Miller, N.J., Shaw, S.W., Turner, K.L.: Parametric amplification in a resonant sensing
array. J. Micromech. Microeng. 22(3), 035004 (2012)
31. Thormann, E., Pettersson, T., Claesson, P.M.: How to measure forces with atomic force
microscopy without significant influence from nonlinear optical lever sensitivity. Rev. Sci.
Instrum. 80(9), 093701 (2009)
32. Hu, S., Raman, A.: Chaos in atomic force microscopy. Phys. Rev. Lett. 96(3), 036107 (2006)
33. Sobreviela, G., Zhao, C., Pandit, M., Do, C., Du, S., Zou, X., Seshia, A.: Parametric noise
reduction in a high-order nonlinear mems resonator utilizing its bifurcation points. J. Microelectromech. Syst. 26(6), 1189–1195 (2017)
34. Zhao, C., Sobreviela, G., Pandit, M., Du, S., Zou, X., Seshia, A.: Experimental observation
of noise reduction in weakly coupled nonlinear MEMS resonators. J. Microelectromech. Syst.
26(6), 1196–1203 (2017)
35. Defoort, M., Taheri-Tehrani, P., Horsley, D.: Exploiting nonlinear amplitude-frequency dependence for temperature compensation in silicon micromechanical resonators. Appl. Phys. Lett.
109(15), 153502 (2016)
36. Chen, D., Wang, Y., Chen, X., Yang, L., Xie, J.: Temperature-frequency drift suppression via
electrostatic stiffness softening in mems resonator with weakened duffing nonlinearity. Appl.
Phys. Lett. 114(2), 023502 (2019)
37. Turner, K.L., Burgner, C.B., Yie, Z., Holtoff, E.: Using nonlinearity to enhance
micro/nanosensor performance. In: 2012 IEEE Sensors, pp. 1–4. IEEE (2012)
38. Burgner, C., Miller, N., Shaw, S., Turner, K.: Parameter sweep strategies for sensing using
bifurcations in MEMS. In: Solid-State Sensor, Actuator, and Microsystems Workshop, Hilton
Head Workshop (2010)
39. Li, L.L., Holthoff, E.L., Shaw, L.A., Burgner, C.B., Turner, K.L.: Noise squeezing controlled
parametric bifurcation tracking of mip-coated microbeam mems sensor for tnt explosive gas
sensing. J. Microelectromech. Syst. 23(5), 1228–1236 (2014)
40. Oropeza-Ramos, L.A., Burgner, C.B., Turner, K.L.: Robust micro-rate sensor actuated by
parametric resonance. Sens. Actuators A: Phys. 152(1), 80–87 (2009)
41. Nitzan, S.H., Zega, V., Li, M., Ahn, C.H., Corigliano, A., Kenny, T.W., Horsley, D.A.: Selfinduced parametric amplification arising from nonlinear elastic coupling in a micromechanical
resonating disk gyroscope. Sci. Rep. 5, 9036 (2015)
42. Endo, D., Yabuno, H., Yamamoto, Y., Matsumoto, S.: Mass sensing in a liquid environment
using nonlinear self-excited coupled-microcantilevers. J. Microelectromech. Syst. 27(5), 774–
779 (2018)
43. Yabuno, H.: Review of applications of self-excited oscillations to highly sensitive vibrational
sensors. ZAMM-J. Appl. Math. Mech./Z. für Angew. Math. und Mech. e201900009 (2019)
44. Hafiz, M., Kosuru, L., Ramini, A., Chappanda, K., Younis, M.: In-plane mems shallow arch
beam for mechanical memory. Micromachines 7(10), 191 (2016)
45. Younis, M.I., Ouakad, H.M., Alsaleem, F.M., Miles, R., Cui, W.: Nonlinear dynamics of mems
arches under harmonic electrostatic actuation. J. Microelectromech. Syst. 19(3), 647–656
(2010)
46. Bajaj, N., Sabater, A.B., Hickey, J.N., Chiu, G.T.-C., Rhoads, J.F.J.: Design and implementation
of a tunable, duffing-like electronic resonator via nonlinear feedback. J. Microelectromech.
Syst. 25(1), 2–10 (2015)
47. Li, L.L., Polunin, P.M., Dou, S., Shoshani, O., Scott Strachan, B., Jensen, J.S., Shaw, S.W.,
Turner, K.L.: Tailoring the nonlinear response of mems resonators using shape optimization.
Appl. Phys. Lett. 110(8), 081902 (2017)
G. Chakraborty and N. Jani
27. Antonio, D., Zanette, D.H., López, D.: Frequency stabilization in nonlinear micromechanical
oscillators. Nat. Commun. 3, 806 (2012)
28. Kaajakari, V., Mattila, T., Oja, A., Seppa, H.: Nonlinear limits for single-crystal silicon
microresonators. J. Microelectromech. Syst. 13(5), 715–724 (2004)
29. Lee, S., Nguyen, C.T.-C.: Phase noise amplitude dependence in self limiting wine-glass disk
oscillators. In: Solid State Sensor, Actuator, and Microsystems Workshop (2004)
30. Yie, Z., Miller, N.J., Shaw, S.W., Turner, K.L.: Parametric amplification in a resonant sensing
array. J. Micromech. Microeng. 22(3), 035004 (2012)
31. Thormann, E., Pettersson, T., Claesson, P.M.: How to measure forces with atomic force
microscopy without significant influence from nonlinear optical lever sensitivity. Rev. Sci.
Instrum. 80(9), 093701 (2009)
32. Hu, S., Raman, A.: Chaos in atomic force microscopy. Phys. Rev. Lett. 96(3), 036107 (2006)
33. Sobreviela, G., Zhao, C., Pandit, M., Do, C., Du, S., Zou, X., Seshia, A.: Parametric noise
reduction in a high-order nonlinear mems resonator utilizing its bifurcation points. J. Microelectromech. Syst. 26(6), 1189–1195 (2017)
34. Zhao, C., Sobreviela, G., Pandit, M., Du, S., Zou, X., Seshia, A.: Experimental observation
of noise reduction in weakly coupled nonlinear MEMS resonators. J. Microelectromech. Syst.
26(6), 1196–1203 (2017)
35. Defoort, M., Taheri-Tehrani, P., Horsley, D.: Exploiting nonlinear amplitude-frequency dependence for temperature compensation in silicon micromechanical resonators. Appl. Phys. Lett.
109(15), 153502 (2016)
36. Chen, D., Wang, Y., Chen, X., Yang, L., Xie, J.: Temperature-frequency drift suppression via
electrostatic stiffness softening in mems resonator with weakened duffing nonlinearity. Appl.
Phys. Lett. 114(2), 023502 (2019)
37. Turner, K.L., Burgner, C.B., Yie, Z., Holtoff, E.: Using nonlinearity to enhance
micro/nanosensor performance. In: 2012 IEEE Sensors, pp. 1–4. IEEE (2012)
38. Burgner, C., Miller, N., Shaw, S., Turner, K.: Parameter sweep strategies for sensing using
bifurcations in MEMS. In: Solid-State Sensor, Actuator, and Microsystems Workshop, Hilton
Head Workshop (2010)
39. Li, L.L., Holthoff, E.L., Shaw, L.A., Burgner, C.B., Turner, K.L.: Noise squeezing controlled
parametric bifurcation tracking of mip-coated microbeam mems sensor for tnt explosive gas
sensing. J. Microelectromech. Syst. 23(5), 1228–1236 (2014)
40. Oropeza-Ramos, L.A., Burgner, C.B., Turner, K.L.: Robust micro-rate sensor actuated by
parametric resonance. Sens. Actuators A: Phys. 152(1), 80–87 (2009)
41. Nitzan, S.H., Zega, V., Li, M., Ahn, C.H., Corigliano, A., Kenny, T.W., Horsley, D.A.: Selfinduced parametric amplification arising from nonlinear elastic coupling in a micromechanical
resonating disk gyroscope. Sci. Rep. 5, 9036 (2015)
42. Endo, D., Yabuno, H., Yamamoto, Y., Matsumoto, S.: Mass sensing in a liquid environment
using nonlinear self-excited coupled-microcantilevers. J. Microelectromech. Syst. 27(5), 774–
779 (2018)
43. Yabuno, H.: Review of applications of self-excited oscillations to highly sensitive vibrational
sensors. ZAMM-J. Appl. Math. Mech./Z. für Angew. Math. und Mech. e201900009 (2019)
44. Hafiz, M., Kosuru, L., Ramini, A., Chappanda, K., Younis, M.: In-plane mems shallow arch
beam for mechanical memory. Micromachines 7(10), 191 (2016)
45. Younis, M.I., Ouakad, H.M., Alsaleem, F.M., Miles, R., Cui, W.: Nonlinear dynamics of mems
arches under harmonic electrostatic actuation. J. Microelectromech. Syst. 19(3), 647–656
(2010)
46. Bajaj, N., Sabater, A.B., Hickey, J.N., Chiu, G.T.-C., Rhoads, J.F.J.: Design and implementation
of a tunable, duffing-like electronic resonator via nonlinear feedback. J. Microelectromech.
Syst. 25(1), 2–10 (2015)
47. Li, L.L., Polunin, P.M., Dou, S., Shoshani, O., Scott Strachan, B., Jensen, J.S., Shaw, S.W.,
Turner, K.L.: Tailoring the nonlinear response of mems resonators using shape optimization.
Appl. Phys. Lett. 110(8), 081902 (2017)