6 Chaotic Vibrations
6.1 Introduction
Mathematical models sometimes behave unpredictably, as do many systems of the
real world. If there are no stochastic components, or if these are considered to be
inessential, we then speak about deterministic chaos, chaotic dynamics or, in case
of vibrating structures, of chaotic vibrations.
This chapter provides an introduction to chaotic vibrations. What do they look
like? How can they be described, where do they appear, and what are their origins?
How can they be detected, predicted, suppressed, or perhaps utilized?
We focus on practical implications and applications. There is a lot of new and
sophisticated mathematics associated with the study of chaos, in particular when it
comes to the search for origins and causes. Without being totally ignorant, we shall
leave most of this to the mathematicians.
Francis C. Moon has made great efforts to turn some of the mathematical
conquests into useful engineering practice and laboratory experiments. His book
(Moon 1987) on chaotic vibrations is intended for applied scientists and engineers,
mainly within the field of mechanics; it is greatly recommended. Other relevant
books are Acheson (1997), Guckenheimer and Holmes (1983), Jackson (1991), Ott
(1993), Parker and Chua (1989), Schuster (1989), Thompson and Bishop (1994),
Thompson and Stewart (1986), Tsonis (1992), Tufillaro et al. (1992), Skiadas
(2016), Skiadas and Skiadas (2016), Awrejcewicz et al. (2016), and Amabili
(2008). Gleick (1987) authored a popular introduction to the subject, including the
exciting history of the birth of chaos science (recommended for the bedside table).
Most material on chaotic vibrations is to be found in scientific papers, some of
which will be referenced when appropriate. Rega, Settimi, and Lenci S (2020)
provides a review of chaotic vibrations of one-dimensional elastic structures like
beams, arches, and cables.
To some extent chaotic vibrations can be viewed simply as yet another phenomenon of which the vibration analyst should be aware. Just like resonance,
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. J. Thomsen, Vibrations and Stability,
https://doi.org/10.1007/978-3-030-68045-9_6
323
6.1 Introduction
Mathematical models sometimes behave unpredictably, as do many systems of the
real world. If there are no stochastic components, or if these are considered to be
inessential, we then speak about deterministic chaos, chaotic dynamics or, in case
of vibrating structures, of chaotic vibrations.
This chapter provides an introduction to chaotic vibrations. What do they look
like? How can they be described, where do they appear, and what are their origins?
How can they be detected, predicted, suppressed, or perhaps utilized?
We focus on practical implications and applications. There is a lot of new and
sophisticated mathematics associated with the study of chaos, in particular when it
comes to the search for origins and causes. Without being totally ignorant, we shall
leave most of this to the mathematicians.
Francis C. Moon has made great efforts to turn some of the mathematical
conquests into useful engineering practice and laboratory experiments. His book
(Moon 1987) on chaotic vibrations is intended for applied scientists and engineers,
mainly within the field of mechanics; it is greatly recommended. Other relevant
books are Acheson (1997), Guckenheimer and Holmes (1983), Jackson (1991), Ott
(1993), Parker and Chua (1989), Schuster (1989), Thompson and Bishop (1994),
Thompson and Stewart (1986), Tsonis (1992), Tufillaro et al. (1992), Skiadas
(2016), Skiadas and Skiadas (2016), Awrejcewicz et al. (2016), and Amabili
(2008). Gleick (1987) authored a popular introduction to the subject, including the
exciting history of the birth of chaos science (recommended for the bedside table).
Most material on chaotic vibrations is to be found in scientific papers, some of
which will be referenced when appropriate. Rega, Settimi, and Lenci S (2020)
provides a review of chaotic vibrations of one-dimensional elastic structures like
beams, arches, and cables.
To some extent chaotic vibrations can be viewed simply as yet another phenomenon of which the vibration analyst should be aware. Just like resonance,
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. J. Thomsen, Vibrations and Stability,
https://doi.org/10.1007/978-3-030-68045-9_6
323