In this paper asymptotic dissipative waves in viscoanelastic media with shape and volumetric memory, previously studied by the author in a more classical way, are studied from the point of view of the double-scale method. Then, a physical interpretation is given of a new (fast) variable ξ , related to the family of hypersurfaces S, across which the solutions or/and some of their derivatives vary steeply, whereas their variation is slow along S and related to the old variables xα (called slow variables). The double-scale method is sketched. The thermodynamical model governing in the three-dimensional case the motion of the rheological media under consideration is presented and many results regarding the propagation of a particular solution into a uniform unperturbed state and the approximation of the first order of the wave front of this solution are given in full detail and reviewed by the double-scale method. Other novel results are worked out. The thermodynamic models for viscoanelastic media with memory are applied in rheology and in several technological sectors.

Asymptotic waves in viscoanelastic media with memory by double-scale method

L. Restuccia
2018-01-01

Abstract

In this paper asymptotic dissipative waves in viscoanelastic media with shape and volumetric memory, previously studied by the author in a more classical way, are studied from the point of view of the double-scale method. Then, a physical interpretation is given of a new (fast) variable ξ , related to the family of hypersurfaces S, across which the solutions or/and some of their derivatives vary steeply, whereas their variation is slow along S and related to the old variables xα (called slow variables). The double-scale method is sketched. The thermodynamical model governing in the three-dimensional case the motion of the rheological media under consideration is presented and many results regarding the propagation of a particular solution into a uniform unperturbed state and the approximation of the first order of the wave front of this solution are given in full detail and reviewed by the double-scale method. Other novel results are worked out. The thermodynamic models for viscoanelastic media with memory are applied in rheology and in several technological sectors.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3121261
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