Negative refraction of Lamb modes: A theoretical study
Abstract
This paper provides a theoretical investigation of negative refraction and focusing of elastic guided waves in a freestanding plate with a steplike thickness change. Under certain conditions, a positive phase velocity (forward) Lamb mode can be converted into a negative phase velocity (backward) mode at such interface, giving rise to negative refraction. A semianalytical model is developed to study the influence of various parameters such as the material Poisson's coefficient, the steplike thickness, the frequency, and the incidence angle. To this end, all the Lamb and shear horizontal propagating modes and also a large number of their inhomogeneous and evanescent counterparts are taken into account. The boundary conditions applied to the stress-displacement fields at the thickness step yields an equation system. Its inversion provides the transmission and reflection coefficients between each mode at the interface. The steplike thickness and Poisson's ratio are shown to be key parameters to optimize the negative refraction process. In terms of material, Duralumin is found to be optimal as it leads to a nearly perfect conversion between forward and backward modes over broad frequency and angular ranges. An excellent focusing ability is thus predicted for a flat lens made of two symmetric thickness steps. A laser ultrasonic experiment quantitatively confirms those theoretical predictions. This study paves the way toward the optimization of elastic devices based on negative refraction, in particular for cloaking or superfocusing purposes.
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