Mixed Frequency Excitation of an Electrostatically Actuated Resonator

We investigate experimentally and theoretically the dynamics of a capacitive resonator under mixed frequency excitation of two AC harmonic signals. The resonator is composed of a proof mass suspended by two cantilever beams. Experimental measurements are conducted using a laser Doppler Vibrometer to reveal the interesting dynamics of the system when subjected to twosource excitation. A nonlinear single-degree-of-freedom model is used for the theoretical investigation. The results reveal combination resonances of additive and subtractive type, which are shown to be promising to increase the bandwidth of the resonator near primary resonance frequency. Our results also demonstrate the ability to shift the combination resonances to much lower or much higher frequency ranges. We also demonstrate the dynamic pull-in instability under mixed frequency excitation.




References:
[1] A. C. Wong and C. C Nguyen, "Micromechanical Mixer-Filters
(“Mixlers”)," J. of Microelectromechanical Sys., vol. 13, no. 1, pp. 100-
112, Feb. 2004.
[2] I. Mahboob, E. Flurin, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi,
"Interconnect-Free Parallel Logic Circuits in a Single Mechanical
Resonator," Nature Communications 2, Article number: 198
doi:10.1038/ncomms1201, Feb. 2011.
[3] I. Mahboob, V. Nier, K. Nishiguchi, K., A. Fujiwara, and H.
Yamaguchi, "Multi-Mode Parametric Coupling in an Electromechanical
Resonator," Appl. Phys. Lett., vol. 103, 153105, 2013.
[4] R. Garcia and E. T. Herruzo, "The Emergence of Multifrequency Force
Microscopy," Nature nanotechnology, vol. 7, no. 4, pp. 217-226, 2012.
[5] D. Hecht, "Multifrequency Acoustooptic Diffraction," IEEE TRANS. ON
Sonics and Ultrasonics, vol. SU-24, no. 1, 1977.
[6] A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations. New York:
Wiley-Interscience, 1979, pp. 183–188.
[7] A. M. Elnagarand and A. F. EI-Bassiouny, "Response of Self-Excited
Three-Degree-of-Freedom Systems to Multifrequency Excitations,"
Inter. J. of Theoretical Phys., vol. 31, no. 8, 1992.
[8] H. Yamaguchi, H. Okamoto, and I. Mahboob, "Coherent Control of
Micro/Nanomechanical Oscillation Using Parametric Mode
Mixing," Appl. Phys. Express, vol. 5, 014001, 2012.
[9] Marc D. Levenson, "Feasibility of Measuring the Nonlinear Index of
Refraction by Third-Order Frequency Mixing," IEEE J. of Quantum
Electronics, vol. 10, no. 2, pp. 110-115, Feb. 1974.
[10] R. Adair, L. L. Chase and S. A. Payne, "Nonlinear Refractive-Index
Measurements of Glasses Using Three-Wave Frequency Mixing," JOSA
B, vol. 4, no. 6, pp. 875-881, 1987.
[11] S. Santos, K. R. Gadelrab, V. Barcons, J. Font, M. Stefancich, and M.
Chiesa, "The Additive Effect of Harmonics on Conservative and
Dissipative Interactions," J. of Appl. Phys., vol. 112, no. 12, 124901,
2012.
[12] A. Erbe and R. H. Blick, "Silicon-on-Insulator Based Nanoresonators for
Mechanical Mixing at Radio Frequencies," IEEE Trans. On Ultrasonics,
Ferroelectrics and Frequency Control, vol. 49, no. 8, pp. 1114-1117,
Aug, 2002.
[13] G. K. Fedder, "CMOS-MEMS Resonant Mixer-Filters," IEEE
International Electron Devices Meeting, Washington, DC, Dec. 2005,
pp. 274-277.
[14] F. Chen, J. Brotz, U. Arslan, C. C. Lo, T. Mukherjee, and G. K. Fedder,
"CMOS-MEMS Resonant RF Mixer-Filters,” Tech. Dig. 18th IEEE Int.
Conf. on Micro Electro Mechanical Systems (MEMS'05), Jan. 2005, pp.
24-7.
[15] M. I. Younis, MEMS Linear and Nonlinear Statics and Dynamics.
Springer, 2011, Ch. 7.
[16] J. F. Roads, S. W. Shaw. K. L. Turner, "Nonlinear Dynamics and Its
Applications in Micro- and Nanoresonators," J. of Dyn. Systems
Measurement, and Control, vol. 132, 2010, p. 14.
[17] I. Kozinsky, H. W. C. Postma, O. Kogan, A. Husain, and M. L. Roukes,
"Basins of attraction of a nonlinear nanomechanical resonator," Physical
Review Lett., vol. 99, no. 20, 2007, 207201.
[18] C. Stambaugh and H. B. Chan, "Noise-activated switching in a driven
nonlinear micromechanical oscillator," Physical Review Lett., vol. 73,
no. 17, 2006, pp. 172-302.
[19] V. Kumar, J. William Boley, Y. Yang, G. T.-C. Chiu, and J. F. Rhoads,
"Modeling, Analysis, and Experimental Validation of a Bifurcation-
Based Microsensor," J. of Microelectromechanical Sys., vol. 21, no. 3,
2012, pp. 549-558.
[20] A. H. Ramini, M. I. Younis, Q. Sue, "A Low-G Electrostatically
Actuated Resonant Switch," Smart Mater. Struct., vol. 22, no. 22,
025006(13pp), Dec. 2013. [21] F. Alsaleem, M. I. Younis, and L. Ruzziconi, "An Experimental and
Theoretical Investigation of Dynamic Pull-in in MEMS Resonators
Actuated Electrostatically," J. of Microelectromechanical Sys., vol. 19,
no. 4, 2010, pp. 794 - 806.
[22] F. Alsaleem, M. I. Younis, and H. Ouakad, "On the Nonlinear
Resonances and Dynamic Pull-in of Electrostatically Actuated
Resonators," J. of Micromechanics and Microengineering, vol. 19, 2009,
045013.