Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Equilibrium Forms Bifurcation of the Nonlinear NEMS/MEMS

Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_162-1



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.


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...

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  1. Bolotin VV (1964) The dynamic stability of elastic systems. Holden-Day, San FranciscozbMATHGoogle Scholar
  2. Chen C, Hone J (2013) Graphene nanoelectromechanical systems. Proc IEEE 101(7):1766–1779CrossRefGoogle Scholar
  3. Doedel EJ, Oldeman BE (2009) AUTO-07P: continuation and bifurcation software for ordinary differential equations. Concordia University, MontrealGoogle Scholar
  4. Eom K, Park HS, Yoon DS, Kwon T (2011) Nanomechanics resonators and their applications in biological/chemical detection. Nanomechanics principles. Phys Rep 503:115–163CrossRefGoogle Scholar
  5. He XQ, Kitiporchai S, Liew KM (2005) Resonance analysis of multi-layered graphene sheets used as nanoscale resonators. Nanotechnology 16:2086–2091CrossRefGoogle Scholar
  6. Keller JB, Stuart A (1969) Bifurcation theory and nonlinear eigenvalue problems. W. A. Benjamin, New YorkGoogle Scholar
  7. Lui Y, Xu Z, Zheng Q (2011) The integral shear effect on graphene multilayer resonators. J Mech Phys Solids 59:1613–1622MathSciNetCrossRefGoogle Scholar
  8. Morozov NF, Berinsky IE, Indeitsev DA, Skubov DY, Shtukin LV (2016) Differential graphene resonator. Dokl Phys 59(7):37–40. (in Russian)Google Scholar
  9. Natsuki T, Shi J, Ni Q (2013) Vibration analysis of nanomechanical mass sensors using double-layered graphene sheets resonators. J Appl Phys 114:904307CrossRefGoogle Scholar
  10. Pelesko JA, Driscoll TA (2005) The effect of the small-aspect-ratio approximation on canonical electrostatic MEMS models. J Eng Math 53:239–252MathSciNetCrossRefGoogle Scholar
  11. Shtukin LV, Berinsky IE, Indeitsev DA, Morozov NF, Skubov DY (2016) Electromechanical models of nanoresonators. Phys Mesomech RAS 19(1):24–30. (in~Russian)Google Scholar
  12. Skubov DY, Khodzhaev KS (2008) Nonlinear electromechanics. Springer, Berlin/HeidelbergzbMATHGoogle Scholar
  13. Van der Zandle AM et al (2010) Large-scale arrays of single-layer graphene resonators. Nano Lett 10:4869–4873CrossRefGoogle Scholar
  14. Zhang WM, Han Y, Peng ZK, Meng G (2014) Electrostatic pull-in instability MEMS/NEMS: a review. Sensor Actuators A Phys 214:187–218CrossRefGoogle Scholar

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute Problems of Mechanical Engineering RASSt. PetersburgRussia
  3. 3.Peter the Great St. Petersburg Polythechnic UniversitySt. PetersburgRussia

Section editors and affiliations

  • Victor A. Eremeyev
    • 1
  1. 1.Gdańsk University of TechnologyGdańskPoland