Estimation of viscoelastic properties in ribbon-shaped homogeneous waveguides by wavenumber analysis and model reduction

Wavenumber based procedures applied to 1D waveguides provide a rigorous framework with an exact signal model that allows for a proper identification of both storage and loss properties independently from the boundary conditions. However, the associated inverse problem is either computationally intense if using a reference solution (e.g. SAFE) or limited to a specific frequency range that depends on the reduced beam model. We propose here to apply the wavenumber-based estimation of isotropic viscoelastic properties to ribbon-shaped homogeneous waveguides, characterized by a rectangular section with slender height-to-width aspect ratio. We show theoretically that considering the ribbon as a thick plate by assuming a model reduction in the height dimension, drastically reduces the wave propagation problem (hence its inverse counterpart) while providing a sufficiently good approximation on the low height-to-wavelength regime. In addition, full-field measurements are performed on an Aluminium and a PVC homogeneous ribbon-shaped waveguide. The experimental dispersive branches (bending and torsion modes) are identified on an ultra-wide frequency range (1 kHz - 1 MHz) using High Resolution Wave Analysis. For both materials, an excellent agreement is observed with the thick plate reduced model, paving the way for wide-band viscoelastic properties identification of ribbon-shaped waveguide.