In this paper, we consider periodic waveguides in the shape of a inhomogeneous string or beam partially supported by a uniform elastic Winkler foundation. A multi-parametric analysis is developed to take into account the presence of internal cutoff frequencies and strong contrast of the problem parameters. This leads to asymptotic conditions supporting non-typical quasi-static uniform or, possibly, linear microscale displacement variations over the high-frequency domain. Macroscale governing equations are derived within the framework of the Floquet-Bloch theory as well as using a high-frequency-type homogenization procedure adjusted to a string with variable parameters. It is found that, for the string problem, the associated macroscale equation is the same as that applying to a string resting on a Winkler foundation. Remarkably, for the beam problem, the macroscale behavior is governed by the same equation as for a beam supported by a two-parameter Pasternak foundation.

Multi-parametric analysis of strongly inhomogeneous periodic waveguideswith internal cutoff frequencies / Kaplunov, J.; Nobili, Andrea. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - (2017), pp. N/A-n/a. [10.1002/mma.3900]

Multi-parametric analysis of strongly inhomogeneous periodic waveguideswith internal cutoff frequencies

NOBILI, Andrea
2017

Abstract

In this paper, we consider periodic waveguides in the shape of a inhomogeneous string or beam partially supported by a uniform elastic Winkler foundation. A multi-parametric analysis is developed to take into account the presence of internal cutoff frequencies and strong contrast of the problem parameters. This leads to asymptotic conditions supporting non-typical quasi-static uniform or, possibly, linear microscale displacement variations over the high-frequency domain. Macroscale governing equations are derived within the framework of the Floquet-Bloch theory as well as using a high-frequency-type homogenization procedure adjusted to a string with variable parameters. It is found that, for the string problem, the associated macroscale equation is the same as that applying to a string resting on a Winkler foundation. Remarkably, for the beam problem, the macroscale behavior is governed by the same equation as for a beam supported by a two-parameter Pasternak foundation.
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Multi-parametric analysis of strongly inhomogeneous periodic waveguideswith internal cutoff frequencies / Kaplunov, J.; Nobili, Andrea. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - (2017), pp. N/A-n/a. [10.1002/mma.3900]
Kaplunov, J.; Nobili, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/1115000
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