### Abstract

Mechanical systems consisting of linear components with many degrees of freedom
and local nonlinearities are frequently met in engineering practice. From.a spatial point
of view, the local nonlinearities constitute only a small part of the mechanical system.
However, their presence can have important consequences for the overall dynamic
behaviour.
The subject of this paper is the long term behaviour of the above systems, excited by
periodic external loads. The number of degrees of freedom of the linear components of
the system is reduced by applying a component mode synthesis technique based on
free-interface eigenmodes and residual flexibility modes. Periodic solutions are
calculated efficiently by solving a two-point boundary value problem using finite
differences. How the periodic solution is influenced by a change in a so-called design
variable of the system is investigated by applying a path following technique. Floquet
multipliers are calculated to determine the local stability of these solutions and to
identify local bifurcation points. The steady-state behaviour is also investigated by
means of standard numerical time integration. In this case the character of the long
term behaviour (peridic, quasi-periodic or chaotic) is identified by caiculation of the
Lyapunov exponents.
The methods outlined above are applied to a harmonically exCited discretized beam
system supported by a one-sided linear spring, which reveals very rich, complex
dynamic behaviour.

Original language | English |
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Title of host publication | Topics in applied mechanics : integration of theory and applications in applied mechanics [2nd National mechanics conference, November 1992, Kerkrade, The Netherlands] |

Editors | J.F. Dijksman, F.T.M. Nieuwstadt |

Place of Publication | Dordrecht |

Publisher | Kluwer Academic Publishers |

Pages | 261-268 |

ISBN (Print) | 0-7923-2442-0 |

Publication status | Published - 1993 |

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## Cite this

Campen, van, D. H., Fey, R. H. B., & Kraker, de, A. (1993). Structural dynamics of mechanical systems with local nonlinearities under periodic excitation. In J. F. Dijksman, & F. T. M. Nieuwstadt (Eds.),

*Topics in applied mechanics : integration of theory and applications in applied mechanics [2nd National mechanics conference, November 1992, Kerkrade, The Netherlands]*(pp. 261-268). Kluwer Academic Publishers.