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A theoretical analysis in the time-domain of wave reflection
ARTICLE IN PRESSJOURNAL OF
SOUND AND
VIBRATION0022-460X/$ - s
doi:10.1016/j.js
Correspond
E-mail addrJournal of Sound and Vibration 298 (2006) 12–29
/locate/jsviA theoretical analysis in the time-domain of wave reflection
on a bone plate
Quentin Grimala, Salah Na??lib,
aLaboratoire d’Imageric Parame?trique, CNRS UMR 7623, Universite? Pierre et marie Curie, 15 rue de l’e?cole de me?decine,
75006 Paris France
bLaboratoire de Me?canique Physique, CNRS UMR 7052 B20A, Faculte? des Sciences et Technologie, Universite? Paris XII-Val de Marne, 61,
Avenue du Ge?ne?ral de Gaulle, 94010 Cre?teil Ce?dex, France
Received 13 December 2004; received in revised form 16 January 2006; accepted 10 April 2006
Available online 7 July 2006Abstract
This paper presents an original method for simulating ultrasonic wave reflection on a fluid-loaded plate. Geometrical
and material parameters used are relevant to the ‘‘axial transmission technique’’ (ATT) setup. Devices based on the ATT
are used for the assessment of cortical bone strength (estimate of a fracture risk). In this work, the cortical bone layer is
represented as a plate of infinite extent surrounded by fluid (soft tissues). A line source and a receiver are placed in the fluid.
Transient waves generated upon reflection at the plate–fluid interfaces are addressed. Analytic Green’s functions are
derived with the generalized ray/Cagniard-de Hoop method. The acoustic response is obtained upon convolution of
Green’s functions with a given source pulse. The method associates each wave amplitude in the time-domain (lateral waves,
reflected body waves, etc.) to a specific term of the final solution. The method is ideally suited to a detailed analysis
of the ultrasonic signal for various geometrical and mechanical parameters. The results presented highlight the potential
of the method for the understanding of wave phenomena involved in the ATT and similar setups. They also bring new
elements that reinforce our theoretical knowledge of the
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