In plane guided modes in soft strips
Résumé
In-plane guided modes propagating in thin soft rectangular waveguides are investigated. These modes result from the coupling between the shear horizontal mode of velocity <latex>v_T</latex> and the plate mode of velocity <latex>v_P</latex> (analogously to the coupling at the interfaces of transverse and longitudinal waves for Lamb modes). Hence, in the low frequency domain, the dispersion curves of these modes are similar to those of Lamb modes in plates of bulk wave velocities <latex>v_P</latex> and <latex>v_T</latex> [1]. As a consequence, the first order in-plane mode propagates backward. Furthermore, if one considers soft materials, <latex>\textiti.e.</latex> incompressible with a Poisson?s ratio of 1/2, the plate velocity is 2<latex>v_T</latex> and consequently the second cut-off frequency is equal to the first one resulting in a Dirac cone at <latex>k=0</latex>. The dispersion curves of those in-plane modes are acquired experimentally in different soft strips made of silicon rubber. The full in-plane displacement is probed for frequencies ranging up to 250 Hz by Digital Image Correlation (DIC) techniques and the full dispersion diagram of the guided modes is retrieved. It is notably found that the fundamental longitudinal mode (pseudo S<latex>₀</latex>) propagates with a velocity of exactly <latex>√3v_T</latex>, independently of the longitudinal wave velocity and regardless of the geometry. In addition, the Dirac cone is clearly evidenced and shifts to slightly lower frequencies due to viscous damping effects. Eventually, a selective chiral excitation is proposed to generate waves allowed to travel solely in a given direction. <latex>\</latex><latex>\</latex> References: <latex>\</latex> [1] Laurent, J., Royer, D., and Prada, C. (2019). arXiv:1907.09813