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Zero group velocity and backward elastic guided modes in homogeneous media
In elastic waveguides, the coupling between shear and compression waves results in complex dispersion effects. Indeed, negative phase velocity modes are observed in most waveguides like plates, tubes or ribbons. These modes, called ’backward’, appear when two branches of neighbouring cut-off frequencies repel each other which can result in a Dirac cone if cut-off frequencies coincide. For low damping material, the minimum frequency of the backward branches corresponds to zero group velocity (ZGV) modes that are associated with narrow local resonances. These resonances are very interesting to evaluate local properties like thickness or Poisson’s ratio. The remarkable properties of negative phase velocity modes and ZGV resonances will be described through direct non-contact measurements on stiff materials using a nanosecond laser ultrasonic technique in the MHz frequency range. Then, the existence of backward modes in soft viscoelastic material will be discussed and illustrated through experiments achieved in the 1 to 100 Hz frequency range using digital image correlation method. Besides, the anisotropy induced by a large static uniaxial strain will be discussed and non-linear elasticity will be considered to model the evolution of mode dispersion.
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[2] Gérardin, Laurent, Legrand, Prada, and Aubry, "Negative reflection of elastic guided waves in chaotic and random scattering media", Scientific Reports, (2019).
[3] Lanoy, Lemoult, Eddi, Prada, "Dirac cones and chiral selection of elastic waves in a soft strip", PNAS (2020)