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The asymptotic analyses of nonlinear waves in rate-dependent media

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Il Nuovo Cimento B (1971-1996)

Summary

High- and low-frequency wave processes are analysed in order to obtain the evolution equations for a rather general nonlinear rate-type (viscoelastic) medium. Moreover, a comparison with the results obtained by Engelbrecht for the standard viscoelastic solid is given. Finally an example of a high-frequency process in a particular nonlinear-linear medium is considered. Such an analysis may be used as a mathematical approach to point out the main features of wave propagation either in certain soft tissues or in certain polymers.

Riassunto

In questo lavoro sono caratterizzati i processi ondosi ad alta e bassa frequenza per una vasta classe di materiali non lineari, in cui siano presenti effetti di memoria, descritti da un’equazione costitutiva di tipo differenziale. Nei due casi sono dedotte le equazioni di evoluzione ed i risultati ottenuti sono confrontati con quelli dedotti da Engelbrecht per un particolare mezzo viscoelastico. Nella parte finale del lavoro si considera un processo ondoso ad alta frequenza in un particolare mezzo non lineare-lineare, che può essere assunto come modello matematico per descrivere certi tipi di tessuti biologici o certe classi di polimeri.

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Authors and Affiliations

  1. Dipartimento di Matematica dell’Università, Via C. Battisti 90, 98100, Messina, Italia

    D. Fusco

  2. Institute of Cybernetics, Estonian Academy of Sciences, Akadeemia St. 21, 200104, Tallinn, Estonia, U.S.S.R.

    J. Engelbrecht

Authors
  1. D. Fusco
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  2. J. Engelbrecht
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Fusco, D., Engelbrecht, J. The asymptotic analyses of nonlinear waves in rate-dependent media. Nuov Cim B 80, 49–61 (1984). https://doi.org/10.1007/BF02899372

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  • DOI: https://doi.org/10.1007/BF02899372

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