Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-24T10:16:57.648Z Has data issue: false hasContentIssue false
  • English
  • Français

Theoretical and experimental study of a pendulum excited by random loads

Part of: Stochastic analysis Applications - Dynamical systems and ergodic theory

Published online by Cambridge University Press:  18 September 2018

L. DOSTAL  and
M.-A. PICK
L. DOSTAL
Affiliation:
Institute of Mechanics and Ocean Engineering, Hamburg University of Technology, 21073 Hamburg, Germany email: dostal@tuhh.de, pick@tuhh.de
M.-A. PICK
Affiliation:
Institute of Mechanics and Ocean Engineering, Hamburg University of Technology, 21073 Hamburg, Germany email: dostal@tuhh.de, pick@tuhh.de
Get access Rights & Permissions [Opens in a new window]

Abstract

Results on the behaviour of a pendulum which is parametrically excited by large amplitude random loads at its pivot are presented, including a novel experimental case study. Thereby, it is dealt with a random excitation by a non-white Gaussian stochastic process with prescribed spectral density. Special focus is devoted to stochastic processes resulting from random sea wave elevation and the question whether random sea waves can lead to rotational motion of the parametrically excited pendulum. The motivation for such an experimental study is energy harvesting from ocean waves.

Keywords

Parametric excitationpendulum dynamicsstochastic averagingexperimental random excitationenergy harvesting

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60H10: Stochastic ordinary differential equations 37N10: Dynamical systems in fluid mechanics, oceanography and meteorology
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Special Issue 5: Stochastic Analysis in Applications , October 2019 , pp. 912 - 927
Copyright
© Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alevras, P. & Yurchenko, D. (2014) Stochastic rotational response of a parametric. Prob. Eng. Mech. 37, 124–131.CrossRefGoogle Scholar
Alevras, P., Brown, I. & Yurchenko, D. (2015) Experimental investigation of a rotating parametric pendulum. Nonlinear Dyn. 81(1–2), 201–213.CrossRefGoogle Scholar
Byrd, P. F. & Friedman, M. D. (1954) Handbook of Elliptic Integrals for Engineers and Scientists, B.G. Teubner, Berlin.CrossRefGoogle Scholar
Dostal, L. & Pick, M.-A (2017) Power generation of a pendulum energy converter excited by random loads. In: Proceedings of the 9th European Nonlinear Oscillations Conference, Budapest, Hungary.Google Scholar
Dostal, L., Korner, K., Kreuzer, E. & Yurchenko, D. (2018) Pendulum energy converter excited by random loads. ZAMM – J. Appl. Math. Mech. 98(3), 349–366. doi:10.1002/zamm.201700007.CrossRefGoogle Scholar
Horton, B., Wiercigroch, M. & Xu, X. (2008) Transient tumbling chaos and damping identification for parametric pendulum. Philos. Trans. R. Soc. A 366(1866), 767–784.CrossRefGoogle ScholarPubMed
Karlin, S. & Taylor, M. H. (1981) A Second Course in Stochastic Processes, Academic Press, New York.Google Scholar
Landau, L. D. & Lifshitz, E. M. (2007) Mechanics, Elsevier, Oxford.Google Scholar
Lingala, N., Sri Namachchivaya, N., Sauer, P. W. & Yeong, H. C. (2017) Random perturbations of nonlinear oscillators: homogenization and large deviations. Int. J. Non-Linear Mech. 94(Suppl. C), 235–250 (Special issue: A conspectus of nonlinear mechanics: a tribute to the oeuvres of Professors G. Rega and F. Vestroni).CrossRefGoogle Scholar
McCormick, M. E. (2013) Ocean Wave Energy Conversion, Courier Corporation, New York.Google Scholar
Najdecka, A., Narayanan, S. & Wiercigroch, M. (2015) Rotary motion of the parametric and planar pendulum under stochastic wave excitation. Int. J. Non-Linear Mech. 71, 30–38.CrossRefGoogle Scholar
Nayfeh, A.H. & Mook, D. T. (2008) Nonlinear Oscillations, John Wiley & Sons, New York.Google Scholar
Sheng, W. & Lewis, A. (2012) Assessment of wave energy extraction from seas: numerical validation. J. Energy Resour. Tech. 134(4), 041701.CrossRefGoogle Scholar
Vaziri, V., Najdecka, A. & Wiercigroch, M. (2014) Experimental control for initiating and maintaining rotation of parametric pendulum. Eur. Phys. J. Spec. Top. 223(4), 795–812.CrossRefGoogle Scholar
Xu, X. & Wiercigroch, M. Approximate analytical solutions for oscillatory and rotational motion of a parametric pendulum. Nonlinear Dyn. 47(1–3), 311–320.Google Scholar
Yurchenko, D. & Alevras, P. (2013) Dynamics of the n-pendulum and its application to a wave energy converter concept. Int. J. Dyn. Control 1(4), 290–299.CrossRefGoogle Scholar
Yurchenko, D. & Alevras, P. (2018) Parametric pendulum based wave energy converter. Mech. Syst. Signal Process. 99, 504–515.CrossRefGoogle Scholar