# In-plane backward and Zero-Group-Velocity guided modes in rigid and soft strips

## TL;DR

This study investigates in-plane guided elastic wave modes in rectangular waveguides, revealing low-frequency backward and zero-group-velocity modes through experiments and simulations, with potential applications in nondestructive testing.

## Contribution

It introduces the observation and analysis of low-frequency backward and ZGV modes in elastic waveguides, supported by experimental and numerical methods, expanding understanding of wave dispersion in soft and rigid strips.

## Key findings

- Backward modes and ZGV resonances occur at very low frequencies in soft ribbons.
- Numerical simulations confirm the existence of these modes at low frequencies.
- Experimental measurements align with theoretical dispersion curves.

## Abstract

Elastic waves guided along bars of rectangular cross section exhibit complex dispersion. This paper studies in-plane modes propagating at low frequencies in thin isotropic rectangular waveguides through experiments and numerical simulations. These modes result from the coupling at the edge between the first order shear horizontal mode $SH_0$ of phase velocity equal to the shear velocity $V_T$ and the first order symmetrical Lamb mode $S_0$ of phase velocity equal to the plate velocity $V_P$. In the low frequency domain, the dispersion curves of these modes are close to those of Lamb modes propagating in plates of bulk wave velocities $V_P$ and $V_T$. The dispersion curves of backward modes and the associated ZGV resonances are measured in a metal tape using non-contact laser ultrasonic techniques. Numerical calculations of in-plane modes in a soft ribbon of Poisson's ratio $\nu \approx 0.5$ confirm that, due to very low shear velocity, backward waves and zero group velocity modes exist at frequencies that are hundreds of times lower than ZGV resonances in metal tapes of the same geometry. The results are compared to theoretical dispersion curves calculated using the method provided in Krushynska and Meleshko (J. Acoust. Soc. Am $129$, 2011).