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Wave Propagation in Linear and Nonlinear Periodic Media pp 161–256Cite as

Map-based approaches for periodic structures

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Part of the book series: CISM Courses and Lectures ((CISM,volume 540))

Abstract

In this chapter the dynamic behavior of periodic structures is dealt with by means of maps. Continuous and discrete models of both linear and nonlinear mechanical systems are considered. The first part of the chapter is devoted to linear problems; general multi-coupled periodic systems are presented and they are dealt with by means of linear maps, namely the transfer matrices of single units. An exhaustive description of the free wave propagation patterns is given on the invariants’. space where propagation domains with qualitatively different character are identified. The problem of minimizing transmitted vibrations through finitely long periodic structures as well as computational issues arising in the wave vector approach are also addressed. The second part of the chapter concerns nonlinear periodic systems, the dynamic analysis of which hinges on nonlinear maps conceived according to two different approaches. At first, a perturbation method is applied to the transfer matrix of a chain of continuous nonlinear beams. Afterwards, nonlinear maps are derived from the governing difference equations of a chain of nonlinear oscillators.

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, SAPIENZA University of Rome, Rome, Italy

    Francesco Romeo

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  1. Francesco Romeo
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Editor information

Editors and Affiliations

  1. University “La Sapienza”, Rome, Italy

    Francesco Romeo

  2. Georgia Institute of Technology, Atlanta, USA

    Massimo Ruzzene

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Romeo, F. (2012). Map-based approaches for periodic structures. In: Romeo, F., Ruzzene, M. (eds) Wave Propagation in Linear and Nonlinear Periodic Media. CISM Courses and Lectures, vol 540. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1309-7_4

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  • DOI: https://doi.org/10.1007/978-3-7091-1309-7_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-1308-0

  • Online ISBN: 978-3-7091-1309-7

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