Abstract
In his 1927 paper in Nature, B. van der Pol described experiments in which an electrical circuit forming a relaxation oscillator was externally forced with continuously varying frequency. The circuit’s response, he found, was entrained to be only at whole submultiples of the forcing frequency, i.e. f/2, f/3, up to f/40. We describe similar results found in an optically actuated MEMS limit cycle oscillator. Doubly supported beams are excited into self-oscillation in their first mode of vibration by illuminating them within an interference field which couples absorption to displacement. While in limit cycle oscillation, they are mechanically shaken out of plane with continuously varying frequency, and the limit cycle response is seen to be entrained to multiples or submultiples of the forcing frequency f/3, f/2, f, 2f, up to 7f.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Rebeiz G (2003) RF MEMS: theory, design, and technology. Wiley, Hoboken
Senturia S (2001) Microsystem design. Springer, New York
Stokes N, Fatah R, Venkatesh F (1990) Self-excitation in fibre-optic microresonator sensors. Sens Actuat A Phys 21(3):369–372
Thundat T, Oden P, Warmac R (1997) Microcantilever sensors. Microscale Thermophys Eng 1(3):185–199
Ilic R, Czaplewski D, Craighead H, Neuzil P, Campagnolo C, Batt C (2000) Mechanical resonant immunospecific biological detector. Appl Phys Lett 77:450–452
Waggoner P, Craighead H (2007) Micro- and nanomechanical sensors for environmental, chemical, and biological detection. Lab Chip 7:1238–1255
Lin L, Howe R, Pisano A (1998) Microelectromechanical filters for signal processing. J Microelectromech Syst 7(3):286–294
Reichenbach R, Zalalutdinov Z, Aubin K, Rand R, Houston B, Parpia J, Craighead H (2005) Third-order intermodulation in a micromechanical thermal mixer. J Microelectromech Syst 14(6):1244–1252
Lee S, Demirci M, Nguyen C-C (2001) A 10-MHz micromechanical resonator pierce reference oscillator for communications. In: Digest of technical papers, the 11th international conference on solid-state sensors and actuators (Transducers’01), Munich, Germany
Adams S, Bertsch F, Shaw K, Hartwell P, Moon F, MacDonald N (1998) Capacitance based tunable resonators. J Micromech Microeng 8(1):15–23
Jenkins D, Cunningham M, Velu G, Remiens D (1997) The use of sputtered ZnO piezoelectric thin films as broad-band microactuators. Sens Actuat A Phys 63(2):135–139
Ilic R, Krylov S, Kondratovich M, Craighead H (2007) Optically actuated nanoelectromechanical oscillators. IEEE J Sel Top Quant Electron 13(2):392–399
Aubin K, Zalalutdinov M, Alan T, Reichenbach R, Rand R, Zehnder A, Parpia J, Craighead H (2004) Limit cycle oscillations in CW laser-driven NEMS. J Microelectromech Syst 13(6):1018–1026
Feng X, White C, Hajimiri A, Roukes M (2008) A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator. Nat Nanotechnol 3:342–346
Rand R (2003) Lecture notes on nonlinear vibrations, version 45. Available online at http://hdl.handle.net/1813/79, Date of Access is March 1, 2012
Van der Pol B, Van der Mark J (1927) Frequency demultiplication. Nature 120(3019):363–364
Storti D, Rand R (1988) Subharmonic entrainment of a forced relaxation oscillator. Int J Non-Linear Mech 23(3):231–239
Zalalutdinov M, Aubin K, Pandey M, Zehnder A, Rand R, Craighead H, Parpia J, Houston B (2003) Frequency entrainment for micromechanical oscillator. Appl Phys Lett 83(16):3281
Zalalutdinov M, Parpia J, Aubin K, Craighead H, Alan T, Zehnder A, Rand R (2003) Hopf bifurcation in a disk-shaped NEMS. In: Proceedings of the 2003 ASME design engineering technical conferences, 19th biennial conference on mechanical vibrations and noise, Chicago, pp 1759–1769
Sekaric L (2003) Studies in NEMS: nanoscale dynamics, energy dissipation, and structural materials. Ph.D. thesis, Cornell University
Carr D, Sekaric L, Craighead H, Parpia J (1999) Measurement of mechanical resonance in nanometer scale silicon wires. Appl Phys Lett 75(7):920–922
Eisley J (1964) Large amplitude vibration of buckled beams and rectangular plates. AIAA J 2(12):2207–2209
Nayfeh A, Mook D (1979) Nonlinear oscillations. Wiley, New York
Pandey M, Aubin K, Zalalutdinov M, Reichenbach R, Zehnder A, Rand R, Craighead H (2006) Analysis of frequency locking in optically driven MEMS resonators. J Microelectromech Syst 15(6):1546–1554
Acknowledgements
This work is supported under NSF grant 0600174 and was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765). This work also made use of the Integrated Advanced Microscopy and Materials facilities of the Cornell Center for Materials Research (CCMR) with support from the National Science Foundation Materials Research Science and Engineering Centers (MRSEC) program (DMR 1120296).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 The Society for Experimental Mechanics
About this paper
Cite this paper
Blocher, D.B., Zehnder, A.T., Rand, R.H. (2013). Frequency Multiplication and Demultiplication in MEMS. In: Shaw, G., Prorok, B., Starman, L. (eds) MEMS and Nanotechnology, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4436-7_9
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4436-7_9
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4435-0
Online ISBN: 978-1-4614-4436-7
eBook Packages: EngineeringEngineering (R0)