Forced Response of Nonlinear Systems Under Combined Harmonic and Random Excitation

Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review

Authors

  • Alwin Förster
  • Lars Panning-von Scheidt
  • Jörg Wallaschek

Research Organisations

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Details

Original languageEnglish
Title of host publicationNonlinear Structures and Systems, Volume 1
Subtitle of host publicationProceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019
EditorsGaetan Kerschen, M.R.W. Brake, Ludovic Renson
PublisherSpringer Nature Switzerland AG
Pages65-80
Number of pages16
Edition1.
ISBN (electronic)978-3-030-12391-8
ISBN (print)978-3-030-12393-2, 978-3-030-12390-1
Publication statusPublished - 29 Jun 2019
Event37th IMAC, A Conference and Exposition on Structural Dynamics, 2019 - Orlando, United States
Duration: 28 Jan 2019 → 31 Jan 2019

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (electronic)2191-5652

Abstract

Mechanical systems are often subjected to different types of excitation. In addition to the commonly considered case of deterministic excitation, random excitation or a combination of both types can occur. The authors present a method to calculate periodic probability density functions of nonlinear mechanical systems under combined harmonic and random excitation. During the calculation, the non-stationary Fokker–Planck equation is solved with a Galerkin-type method. The method uses combined orthogonal, time dependent polynomial as well as harmonic correction terms to reshape an initial guess of the probability density function. It can be used to calculate the stochastic behavior of smaller multi-degree of freedom systems. The applicability is demonstrated using different nonlinear mechanical systems, whereby the results of Monte-Carlo simulations validate the method.

Keywords

    Combined excitation, In-stationary Fokker–Planck equation, Periodic, Probability density function, Random excitation

ASJC Scopus subject areas

Cite this

Forced Response of Nonlinear Systems Under Combined Harmonic and Random Excitation. / Förster, Alwin; Panning-von Scheidt, Lars; Wallaschek, Jörg.
Nonlinear Structures and Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019. ed. / Gaetan Kerschen; M.R.W. Brake; Ludovic Renson. 1. ed. Springer Nature Switzerland AG, 2019. p. 65-80 (Conference Proceedings of the Society for Experimental Mechanics Series).

Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review

Förster, A, Panning-von Scheidt, L & Wallaschek, J 2019, Forced Response of Nonlinear Systems Under Combined Harmonic and Random Excitation. in G Kerschen, MRW Brake & L Renson (eds), Nonlinear Structures and Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019. 1. edn, Conference Proceedings of the Society for Experimental Mechanics Series, Springer Nature Switzerland AG, pp. 65-80, 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, Orlando, United States, 28 Jan 2019. https://doi.org/10.1007/978-3-030-12391-8_7
Förster, A., Panning-von Scheidt, L., & Wallaschek, J. (2019). Forced Response of Nonlinear Systems Under Combined Harmonic and Random Excitation. In G. Kerschen, M. R. W. Brake, & L. Renson (Eds.), Nonlinear Structures and Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019 (1. ed., pp. 65-80). (Conference Proceedings of the Society for Experimental Mechanics Series). Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-030-12391-8_7
Förster A, Panning-von Scheidt L, Wallaschek J. Forced Response of Nonlinear Systems Under Combined Harmonic and Random Excitation. In Kerschen G, Brake MRW, Renson L, editors, Nonlinear Structures and Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019. 1. ed. Springer Nature Switzerland AG. 2019. p. 65-80. (Conference Proceedings of the Society for Experimental Mechanics Series). doi: 10.1007/978-3-030-12391-8_7
Förster, Alwin ; Panning-von Scheidt, Lars ; Wallaschek, Jörg. / Forced Response of Nonlinear Systems Under Combined Harmonic and Random Excitation. Nonlinear Structures and Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019. editor / Gaetan Kerschen ; M.R.W. Brake ; Ludovic Renson. 1. ed. Springer Nature Switzerland AG, 2019. pp. 65-80 (Conference Proceedings of the Society for Experimental Mechanics Series).
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