Definition
Theory of bifurcation boundary problem is well represented in the book written by Keller Joseph B and Antman Stuart [13]. Conception of bifurcation consists in changing of number and stability at monotonous change of characteristic parameter. The point of parameter where this bifurcation takes place is named as branching point.
Introduction
In recent years, great interest of physicists, biologists, and electrical engineers aroused the development of micro- and nanotechnology due to the possibility of sensors production capable for nano- and microscale measurements of physical and biological parameters (Eom et al. 2011; He et al. 2005; Lui et al. 2011; Natsuki et al. 2013; Van der Zandle et al. 2010; Chen and Hone 2013) such as molecular weight, quantum state, properties of biochemical reactions, and others. Nanomechanical sensors...
This is a preview of subscription content, log in via an institution to check access.
References
Bolotin VV (1964) The dynamic stability of elastic systems. Holden-Day, San Francisco
Chen C, Hone J (2013) Graphene nanoelectromechanical systems. Proc IEEE 101(7):1766–1779
Doedel EJ, Oldeman BE (2009) AUTO-07P: continuation and bifurcation software for ordinary differential equations. Concordia University, Montreal
Eom K, Park HS, Yoon DS, Kwon T (2011) Nanomechanics resonators and their applications in biological/chemical detection. Nanomechanics principles. Phys Rep 503:115–163
He XQ, Kitiporchai S, Liew KM (2005) Resonance analysis of multi-layered graphene sheets used as nanoscale resonators. Nanotechnology 16:2086–2091
Keller JB, Stuart A (1969) Bifurcation theory and nonlinear eigenvalue problems. W. A. Benjamin, New York
Lui Y, Xu Z, Zheng Q (2011) The integral shear effect on graphene multilayer resonators. J Mech Phys Solids 59:1613–1622
Morozov NF, Berinsky IE, Indeitsev DA, Skubov DY, Shtukin LV (2016) Differential graphene resonator. Dokl Phys 59(7):37–40. (in Russian)
Natsuki T, Shi J, Ni Q (2013) Vibration analysis of nanomechanical mass sensors using double-layered graphene sheets resonators. J Appl Phys 114:904307
Pelesko JA, Driscoll TA (2005) The effect of the small-aspect-ratio approximation on canonical electrostatic MEMS models. J Eng Math 53:239–252
Shtukin LV, Berinsky IE, Indeitsev DA, Morozov NF, Skubov DY (2016) Electromechanical models of nanoresonators. Phys Mesomech RAS 19(1):24–30. (in~Russian)
Skubov DY, Khodzhaev KS (2008) Nonlinear electromechanics. Springer, Berlin/Heidelberg
Van der Zandle AM et al (2010) Large-scale arrays of single-layer graphene resonators. Nano Lett 10:4869–4873
Zhang WM, Han Y, Peng ZK, Meng G (2014) Electrostatic pull-in instability MEMS/NEMS: a review. Sensor Actuators A Phys 214:187–218
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer-Verlag GmbH Germany
About this entry
Cite this entry
Morozov, N.F., Indeitsev, D.A., Skubov, D.Y., Shtukin, L.V. (2018). Equilibrium Forms Bifurcation of the Nonlinear NEMS/MEMS. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_162-1
Download citation
DOI: https://doi.org/10.1007/978-3-662-53605-6_162-1
Received:
Accepted:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-53605-6
Online ISBN: 978-3-662-53605-6
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering