Parametric resonance and parametric amplification are important phenomena that are relevant to many fields of science. For mechanical systems, parametric driving typically involve modulating the spring constant [1, 2] or the moment of inertia near twice the natural frequency of the system. Parametric amplification has proved useful in improving the signal to noise before transduction of the mechanical displacement into an electrical signal [1]. Apart from amplifying a signal, parametric pumping can also reduce the linewidth of the resonance response, opening up new opportunities for biochemical detection using micro- and nano-mechanical devices in viscous environments [3]. Recently the sharp jump in the parametric response of micromechanical oscillators at subcritical bifurcation was used for accurate determination of the natural frequency to deduce device parameters [4].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D. Rugar and P. Grutter, Phys. Rev. Lett. 67, 699 (1991).
D. W. Carr, S. Evoy, L. Sekaric, et al., Appl. Phys. Lett. 77, 1545 (2000).
L. Sekaric, M. Zalalutdinov, R. B. Bhiladvala, et al., Appl. Phys. Lett. 81, 2641 (2002).
W. H. Zhang, R. Baskaran, and K. L. Turner, Sensors and Actuators a-Physical 102, 139 (2002).
M. I. Dykman and M. A. Krivoglaz, Zh. Eksper. Teor. Fiz. 77, 60 (1979).
M. I. Dykman, C. M. Maloney, V. N. Smelyanskiy, et al., Phys. Rev. E 57, 5202 (1998).
L. J. Lapidus, D. Enzer, and G. Gabrielse, Phys. Rev. Lett. 83, 899 (1999).
J. S. Aldridge and A. N. Cleland, Phys. Rev. Lett. 94, 156403 (2005).
C. Stambaugh and H. B. Chan, Phys. Rev. B 73, 172302 (2006).
R. L. Badzey and P. Mohanty, Nature 437, 995 (2005).
R. Almog, S. Zaitsev, O. Shtempluck, et al., Appl. Phys. Lett. 90, 013508 (2007).
E. V. Sukhorukov and A. N. Jordan, Phys. Rev. Lett. 98, 136803 (2007).
I. Siddiqi, R. Vijay, F. Pierre, et al., Phys. Rev. Lett. 93, 207002 (2004).
I. Siddiqi, R. Vijay, F. Pierre, C. M. Wilson, L. Frunzio, M. Metcalfe, C. Rigetti, R. J. Schoelkopf, M. H. Devoret, D. Vion, and D.Esteve, Phys. Rev. Lett. 94, 027005 (2005).
K. Kim, M. S. Heo, K. H. Lee, et al., Phys. Rev. A 72, 053402 (2005).
K. Kim, M. S. Heo, K. H. Lee, et al., Phys. Rev. Lett. 96, 150601 (2006).
L. D. Landau and E. M. Lifshitz, Mechanics, Course of theoretical physics vol.1, (1969).
I. Siddiqi, R. Vijay, F. Pierre, et al., cond-mat/0507248 (2005).
M. I. Dykman, I. B. Schwartz, and M. Shapiro, Phys. Rev. E 72, 021102 (2005).
D. Ryvkine and M. I. Dykman, Phys. Rev. E 74, 061118 (2006).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Chan, H., Stambaugh, C. (2009). Activated Switching in a Parametrically Driven Micromechanical Torsional Oscillator. In: In, V., Longhini, P., Palacios, A. (eds) Applications of Nonlinear Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85632-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-85632-0_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85631-3
Online ISBN: 978-3-540-85632-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)