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2012 | OriginalPaper | Buchkapitel

1. An Introduction to Parametric Resonance

verfasst von : Jonatan Peña-Ramírez, Rob H. B. Fey, Henk Nijmeijer

Erschienen in: Parametric Resonance in Dynamical Systems

Verlag: Springer New York

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Abstract

In many engineering, physical, electrical, chemical, and biological systems, oscillatory behavior of the dynamic system due to periodic excitation is of great interest. Two kinds of oscillatory responses can be distinguished: forced oscillations and parametric oscillations. Forced oscillations appear when the dynamical system is excited by a periodic input. If the frequency of an external excitation is close to the natural frequency of the system, then the system will experience resonance, i.e. oscillations with a large amplitude.

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Literatur
1.
Zurück zum Zitat Amabili, M., Paidoussis, M. P.: Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Applied Mechanics Reviews, 56(4):349–381, (2003).CrossRef Amabili, M., Paidoussis, M. P.: Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Applied Mechanics Reviews, 56(4):349–381, (2003).CrossRef
2.
Zurück zum Zitat Armstrong, E. H.: Some recent developments of regenerative circuits. Proceedings of the Institute of Radio Engineers, 10:244–260, (1922). Armstrong, E. H.: Some recent developments of regenerative circuits. Proceedings of the Institute of Radio Engineers, 10:244–260, (1922).
3.
Zurück zum Zitat Arscott, F.: Periodic differential equations. Pergamon Press. New York, (1964).MATH Arscott, F.: Periodic differential equations. Pergamon Press. New York, (1964).MATH
4.
Zurück zum Zitat Ataka, H.: On superregeneration of an ultra-short-wave receiver. Proceedings of the Institute of Radio Engineers, 23(8):841–884, (1935). Ataka, H.: On superregeneration of an ultra-short-wave receiver. Proceedings of the Institute of Radio Engineers, 23(8):841–884, (1935).
5.
Zurück zum Zitat Barrow, W. L., Smith, D. B., Baumann, F. W.: A further study of oscillatory circuits having periodically varying parameters. Journal of The Franklin Institute, 221(3):403–416, (1936).CrossRef Barrow, W. L., Smith, D. B., Baumann, F. W.: A further study of oscillatory circuits having periodically varying parameters. Journal of The Franklin Institute, 221(3):403–416, (1936).CrossRef
6.
Zurück zum Zitat Biran, A.: Ship hydrostatics and stability. Butterworth-Heinemann. Oxford, (2003). Biran, A.: Ship hydrostatics and stability. Butterworth-Heinemann. Oxford, (2003).
7.
Zurück zum Zitat Broer, H. W., Levi, M.: Geometrical aspects of stability theory for Hill’s equations. Archive for rational mechanics and analysis, 131(3):225–240, (1995).CrossRefMathSciNetMATH Broer, H. W., Levi, M.: Geometrical aspects of stability theory for Hill’s equations. Archive for rational mechanics and analysis, 131(3):225–240, (1995).CrossRefMathSciNetMATH
8.
Zurück zum Zitat Brown, D. K.: The way of a ship in the midst of the sea: the life and work of William Froude. Periscope Publishing Ltd. ISBN-10: 1904381405, (2006). Brown, D. K.: The way of a ship in the midst of the sea: the life and work of William Froude. Periscope Publishing Ltd. ISBN-10: 1904381405, (2006).
9.
Zurück zum Zitat France, W. N., Levadou, M., Trakle, T. W., Paulling, J. R., Michel, R. K., Moore, C.: An investigation of head-sea parametric rolling and its influence on container lashing systems, Marine Technology, 40(1):1–19, (2003). France, W. N., Levadou, M., Trakle, T. W., Paulling, J. R., Michel, R. K., Moore, C.: An investigation of head-sea parametric rolling and its influence on container lashing systems, Marine Technology, 40(1):1–19, (2003).
10.
Zurück zum Zitat Galeazzi, R.: Autonomous supervision and control of parametric roll resonance. Ph.D. Thesis, Kongens Lyngby, Denmark, (2009). Galeazzi, R.: Autonomous supervision and control of parametric roll resonance. Ph.D. Thesis, Kongens Lyngby, Denmark, (2009).
11.
Zurück zum Zitat Holden, C., Galeazzi, R., Rodríguez, C., Perez, T., Fossen, T. I., Blanke, M., Neves, M. A. S.: Nonlinear container ship model for the study of parametric roll resonance. Modeling, identification and control, 28(4):87–103, (2007).CrossRef Holden, C., Galeazzi, R., Rodríguez, C., Perez, T., Fossen, T. I., Blanke, M., Neves, M. A. S.: Nonlinear container ship model for the study of parametric roll resonance. Modeling, identification and control, 28(4):87–103, (2007).CrossRef
13.
Zurück zum Zitat Jeffreys, H.: The free oscillation of water in an elliptical lake. Proceedings of the London Mathematical Society (second edition), 23:455–476, (1923). Jeffreys, H.: The free oscillation of water in an elliptical lake. Proceedings of the London Mathematical Society (second edition), 23:455–476, (1923).
14.
Zurück zum Zitat Lamb, H.: Hydrodynamics. Sixth edition. Cambridge University Press. Cambridge, United Kingdom (1945).MATH Lamb, H.: Hydrodynamics. Sixth edition. Cambridge University Press. Cambridge, United Kingdom (1945).MATH
15.
Zurück zum Zitat Markevich, N. I., Sel’kov, E. E.: Parametric resonance and amplification in excitable membranes. The Hodgkin-Huxley model. Journal of Theoretical Biology, 140(1):27–38, (1989).CrossRefMathSciNet Markevich, N. I., Sel’kov, E. E.: Parametric resonance and amplification in excitable membranes. The Hodgkin-Huxley model. Journal of Theoretical Biology, 140(1):27–38, (1989).CrossRefMathSciNet
16.
Zurück zum Zitat Mathieu, É.: Mémoire sur le mouvement vibratoire d’une membrane de forme elliptique. Journal of Mathematics, 13:137–203, (1868).MATH Mathieu, É.: Mémoire sur le mouvement vibratoire d’une membrane de forme elliptique. Journal of Mathematics, 13:137–203, (1868).MATH
17.
Zurück zum Zitat McLachlan, N. W.: Theory and Applications of Mathieu Functions. Oxford Press, London (1951). McLachlan, N. W.: Theory and Applications of Mathieu Functions. Oxford Press, London (1951).
18.
Zurück zum Zitat 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. Sensors and Actuators A: Physical, 142(1):306–315, (2008).CrossRef 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. Sensors and Actuators A: Physical, 142(1):306–315, (2008).CrossRef
19.
Zurück zum Zitat Nayfeh, A. H., Mook, D. T.: Nonlinear Oscillations. John Wiley %26 Sons. New York, (1979). Nayfeh, A. H., Mook, D. T.: Nonlinear Oscillations. John Wiley %26 Sons. New York, (1979).
20.
Zurück zum Zitat Piccardo, G., Tubino, F.: Parametric resonance of flexible footbridges under crowd-induced lateral excitation. Journal of Sound and Vibration, 311:353–371, (2008).CrossRef Piccardo, G., Tubino, F.: Parametric resonance of flexible footbridges under crowd-induced lateral excitation. Journal of Sound and Vibration, 311:353–371, (2008).CrossRef
21.
Zurück zum Zitat Rhoads, J. F., Shaw, S. W., Turner, K. L.: Nonlinear dynamics and its applications in micro- and nanoresonators. Journal of Dynamic Systems, Measurement, and Control, 132(034001):1–14, (2010). Rhoads, J. F., Shaw, S. W., Turner, K. L.: Nonlinear dynamics and its applications in micro- and nanoresonators. Journal of Dynamic Systems, Measurement, and Control, 132(034001):1–14, (2010).
22.
23.
Zurück zum Zitat Sahu, S. K. and Datta, P. K.: Research advances in the dynamic stability behavior of plates and shells: 1987–2005 Part I: Conservative Systems. Applied Mechanics Reviews, 60:65–75, (2007).CrossRef Sahu, S. K. and Datta, P. K.: Research advances in the dynamic stability behavior of plates and shells: 1987–2005 Part I: Conservative Systems. Applied Mechanics Reviews, 60:65–75, (2007).CrossRef
24.
Zurück zum Zitat Seyranian, A. P.: The swing: parametric resonance. Journal of Applied Mathematics and Mechanics, 68(5):757–764, (2004).CrossRefMathSciNet Seyranian, A. P.: The swing: parametric resonance. Journal of Applied Mathematics and Mechanics, 68(5):757–764, (2004).CrossRefMathSciNet
25.
Zurück zum Zitat Taylor, G. I.: Tidal oscillations in gulfs and rectangular basins. Proceedings of the London Mathematical Society, 20:148–181, (1920).MathSciNetMATH Taylor, G. I.: Tidal oscillations in gulfs and rectangular basins. Proceedings of the London Mathematical Society, 20:148–181, (1920).MathSciNetMATH
26.
Zurück zum Zitat Tondl, A., Ruijgrok, T., Verhulst, F., Nabergoj, R.: Autoparametric resonance in mechanical systems. Cambridge University Press, Cambridge, United Kingdom (2000).MATH Tondl, A., Ruijgrok, T., Verhulst, F., Nabergoj, R.: Autoparametric resonance in mechanical systems. Cambridge University Press, Cambridge, United Kingdom (2000).MATH
27.
Zurück zum Zitat van der Pol B, Strutt, M. J. O.: On the stability of the solutions of Mathieu’s equation. Philosophical Magazine, Series 7, 5(27):18–38, (1928).MATH van der Pol B, Strutt, M. J. O.: On the stability of the solutions of Mathieu’s equation. Philosophical Magazine, Series 7, 5(27):18–38, (1928).MATH
28.
Zurück zum Zitat Whittaker, E. T., Watson, G. N.: A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions. Cambridge University Press, 3rd edition, Cambridge, United Kingdom (1920). Whittaker, E. T., Watson, G. N.: A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions. Cambridge University Press, 3rd edition, Cambridge, United Kingdom (1920).
Metadaten
Titel
An Introduction to Parametric Resonance
verfasst von
Jonatan Peña-Ramírez
Rob H. B. Fey
Henk Nijmeijer
Copyright-Jahr
2012
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-1043-0_1

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