Top

Published in:

2017 | OriginalPaper | Chapter

On Application Melnikov Method to Detecting the Edge of Chaos for a Micro-Cantilever

Authors : J. Xie, S.-H. He, Z.-H. Liu, Y. Chen

Published in: New Advances in Mechanisms, Mechanical Transmissions and Robotics

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, Melnikov method is employed to detecting the edge of chaos for a micro-cantilever. The difficulties arising from the integrals in Melnikov method are refrained through using MATLAB/Simulink. The edge of chaos plotted on a two parameter plane indicate that the condition of chaos occurrence derived from Melnikov method is compact for some system parameters, but is conservative for the others. Therefore, applying Melnikov method to detecting edge of chaos is far from perfect method.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Novel Speed Increaser Used in Counter-Rotating Wind Turbines

next chapter Use of the Structomatic Method to Perform the Forward Kinematic and Kinetostatic Analyses of a Hydraulic Excavator

Rhoads, J.F., Shaw, S.W., Turner, K.L.: Nonlinear dynamics and its applications in micro- and nanoresonators. J. Dyn. Syst. Meas. Control 132(3), 034001–34002 (2010)CrossRef

Seleim, A., Towfighian, S., Delande, E., Abdel-Rahman, E., Heppler, G.: Dynamics of a close-loop controlled MEMS resonator 69(1), 615–633 (2012)

Langton, C.G.: Computation at the edge of chaos: phase transition and emergent computation. Phys. D 42, 12–37 (1990)MathSciNetCrossRef

Melnikov, V.K.: On the stability of the centre for time periodic perturbations. Trans. Moscow Math. 12, 1–57 (1963)

Awrejcewicz, J., Holicke, M.: M: Smooth and Nonsmooth High Dimensional Chaos and the Melnikov-Type Methods. World Scientific Publishing Co. Pre Ltd, Singapore (2007)CrossRefMATH

Haghighi, H.S., Markazi, A.H.D.: Chaos prediction and control in MEMS resonators. Commun. Nonlinear Sci. Numer. Simul. 15(10), 3091–3099 (2010)CrossRef

Siewe, M.S., Hegazy, U.H.: Homoclinic bifurcation and chaos control in MEMS resonators. Appl. Math. Model. 35(12), 5533–5552 (2011)MathSciNetCrossRefMATH

Han, J.-X., Zhang, Q.-C., Wang, W.: Design considerations on large amplitude vibration of a doubly clamped microresonator with two symmetrically located electrodes. Commun. Nonlinear Sci. Numer. Simul. 22(1–3), 492–510 (2015)CrossRef

Maani Miandoab, E., Pishkenari, H.N., Yousefi-Koma, A., Tajaddodianfar, F.: Chaos prediction in MEMS-NEMS resonators. Int. J. Eng. Sci. 82, 74–83 (2014)

10.

Tajaddodianfar, F., Nejat Pishkenari, H., Hairi Yazdi, M.R.: Prediction of chaos in electrostatically actuated arch micro-nano resonators: Analytical approach. Commun. Nonlinear Sci. Numer. Simul. 30(1–3), 182–195 (2016)

11.

Ling, F.H., Bao, G.W.: A numerical implementation of Melnikov’s method. Phys. Lett. A 122(8), 413–417 (1987)CrossRef

12.

Bruhn, B., Koch, B.P.: Homoclinc and heteroclinic bifurcations in rf SQUIDS. Zeitschrift fur Naturforschung 43, 930–938 (1988)MathSciNet

13.

Yagasaki, K.: Chaos in a pendulum with feedback control. Nonlinear Dyn. 6, 125–142 (1994)CrossRef

14.

Zhang, W.-M., Meng, G.: Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitation in MEMS. Sens. Actuators A 199(2), 291–299 (2005)MathSciNetCrossRef

15.

Jimenez-Triana, A., Zhu, G.-C., Saydy, L.: Chaos synchronization of an electrostatic MEMS resonator in the presence of parametric uncertainties. In: Proceedings of 2011 American Control Conference, San Francisco, CA, USA, pp. 5115–5120 (2011)

16.

Mestrom, R.M.C., Fey, R.H.B., van Beek, J.T.M., Phan, K.L., Nijmeijer, H.: Modelling the dynamics of a MEMS resonator: simulations and experiments. Sens. Actuators A 142, 306–315 (2008)CrossRef

17.

Robinson, R.C.: An Introduction to Dynamical Systems: Continuous and Discrete. Pearson Education Inc. (2004)

18.

Xu, P.-C., Jing, Z.-J.: Heteroclinic orbits and chaotic regions for Josephson system. J. Math. Anal. Appl. 376(1), 103–122 (2011)MathSciNetCrossRefMATH

19.

Doroshin, A.V.: Heteroclinic dynamics and attitude motion chaotization of coaxial bodies and dual-spin spacecraft. Commun. Nonlinear Sci. Numer. Simul. 17(3), 1460–1474 (2012)MathSciNetCrossRefMATH

20.

Wiggins, S.: Introduction to Applied Nonlinear dynamical Systems and Chaos. Springer (2003)

Title: On Application Melnikov Method to Detecting the Edge of Chaos for a Micro-Cantilever
Authors: J. Xie
S.-H. He
Z.-H. Liu
Y. Chen
Publisher: Springer International Publishing
Book: New Advances in Mechanisms, Mechanical Transmissions and Robotics
Print ISBN: 978-3-319-45449-8

Electronic ISBN: 978-3-319-45450-4

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-45450-4_16

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Premium Partners