The dynamic nonlinear problem of wave propagation in infinitely long hysteretic beams under bending is addressed. Such a problem is tackled by proposing an asymptotic treatment based on the method of multiple scales. The equations of motion are obtained reducing the three-dimensional-continuum model to the one-dimensional plane beam problem via the cross-section rigidity constraint, and describing the hysteresis via a nonlinear viscoelasticmaterial model, which can be easily tuned to obtain either hardening or softening characteristic responses. Geometric nonlinearities are not taken into account. In addition to the perturbation treatment of the wave equations with hysteretic nonlinearity, which provided the slow amplitude and phase modulations with time and space, a number of numerical tests are presented to show how the hysteretic nonlinear response can give rise to dissipative nonlinear bending waves. The limit case of zero dissipation is also investigated to shed light on the distinct effects of viscolelasticity.

Propagation of nonlinear bending waves in hysteretic beams / Pau, Annamaria; Carboni, Biagio; Lacarbonara, Walter; Formica, Giovanni. - In: INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING. - ISSN 1543-1649. - 6:20(2022), pp. 43-59. [10.1615/IntJMultCompEng.2022042439]

Propagation of nonlinear bending waves in hysteretic beams

Annamaria Pau
;
Biagio Carboni;Walter Lacarbonara;
2022

Abstract

The dynamic nonlinear problem of wave propagation in infinitely long hysteretic beams under bending is addressed. Such a problem is tackled by proposing an asymptotic treatment based on the method of multiple scales. The equations of motion are obtained reducing the three-dimensional-continuum model to the one-dimensional plane beam problem via the cross-section rigidity constraint, and describing the hysteresis via a nonlinear viscoelasticmaterial model, which can be easily tuned to obtain either hardening or softening characteristic responses. Geometric nonlinearities are not taken into account. In addition to the perturbation treatment of the wave equations with hysteretic nonlinearity, which provided the slow amplitude and phase modulations with time and space, a number of numerical tests are presented to show how the hysteretic nonlinear response can give rise to dissipative nonlinear bending waves. The limit case of zero dissipation is also investigated to shed light on the distinct effects of viscolelasticity.
2022
wave propagation, guided waves, bending waves, hysteretic materials, method of multiple scales, perturbation approach
01 Pubblicazione su rivista::01a Articolo in rivista
Propagation of nonlinear bending waves in hysteretic beams / Pau, Annamaria; Carboni, Biagio; Lacarbonara, Walter; Formica, Giovanni. - In: INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING. - ISSN 1543-1649. - 6:20(2022), pp. 43-59. [10.1615/IntJMultCompEng.2022042439]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1652020
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