Abstract
Parametric excitation in a mechnical system may occur if a parameter of the system becomes time-dependent. The mathematical model for this type of excitation is characterized by terms in the differential equations which have time-dependent coefficients. A standard example of an equation which displays parametric excitation is the Mathieu equation. In this paper two systems will be considered in more detail: a pendulum and a stretched string both with varying length. The attention will be focused to the (unstability) of the equilibrium position (trivial solution). Also finite amplitude motions will be considered, for the description of which however additional nonlinear terms are taken into account.
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References
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Second edition, Springer Universitext, 1996.
A.H. Nayfeh and D.T. Mook, Nonlinear Oscillations, John Wiley, 1979.
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F. Melde, Über die Erregung stehender Wellen eines fadenförmigen Körpers, Pogg. Ann. d. Phys. Bd. III, pp. 193–215, 1860.
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© 1997 Springer Science+Business Media Dordrecht
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Van der Burgh, A.H.P. (1997). Parametric Excitation in Mechanical Systems. In: van Groesen, E., Soewono, E. (eds) Differential Equations Theory, Numerics and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5157-3_1
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DOI: https://doi.org/10.1007/978-94-011-5157-3_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6168-1
Online ISBN: 978-94-011-5157-3
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