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Ultrasonics. 2015 Jan;55:85-91. doi: 10.1016/j.ultras.2014.08.001. Epub 2014 Aug 13.

Reciprocity principle for scattered fields from discontinuities in waveguides.

Author information

1
Department of Structural and Geotechnical Engineering, La Sapienza University of Rome, Via Gramsci 53, 00197 Roma, Italy. Electronic address: annamaria.pau@uniroma1.it.
2
Department of Structural and Geotechnical Engineering, La Sapienza University of Rome, Via Gramsci 53, 00197 Roma, Italy. Electronic address: danilo.capecchi@uniroma1.it.
3
Department of Structural and Geotechnical Engineering, La Sapienza University of Rome, Via Eudossiana 18, 00185 Roma, Italy. Electronic address: vestroni@uniroma1.it.

Abstract

This study investigates the scattering of guided waves from a discontinuity exploiting the principle of reciprocity in elastodynamics, written in a form that applies to waveguides. The coefficients of reflection and transmission for an arbitrary mode can be derived as long as the principle of reciprocity is satisfied at the discontinuity. Two elastodynamic states are related by the reciprocity. One is the response of the waveguide in the presence of the discontinuity, with the scattered fields expressed as a superposition of wave modes. The other state is the response of the waveguide in the absence of the discontinuity oscillating according to an arbitrary mode. The semi-analytical finite element method is applied to derive the needed dispersion relation and wave mode shapes. An application to a solid cylinder with a symmetric double change of cross-section is presented. This model is assumed to be representative of a damaged rod. The coefficients of reflection and transmission of longitudinal waves are investigated for selected values of notch length and varying depth.

KEYWORDS:

Damage; Guided waves; Principle of reciprocity; Scattered fields

PMID:
25172113
DOI:
10.1016/j.ultras.2014.08.001
[Indexed for MEDLINE]

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