High Resolution Wavenumber Analysis (HRWA) for the mechanical characterisation of viscoelastic beams

The High-Resolution Wavenumber Analysis (HRWA) is presented. It identifies complex wavenumbers and amplitudes of waves composing the harmonic response of a beam. Based on the frequency dependence of these wavenumbers, experimental dispersion equations of various beam mechanisms (e.g bending, torsion) can be retrieved. The HRWA method is compared to the Mc Daniel and the Inverse Wave Correlation (IWC) methods. It overcomes some drawbacks of these methods: the wavenumber resolution is enhanced. Also, the wavenumber search problem is expressed as a linear problem, making the method computationally efficient. A number of wavenumbers can be identified automatically, thanks to a statistical criterion. First, the noise sensitivity of each method is investigated in the basis of synthesised measurements. For this criterion, the HRWA and Mc Daniel method performances are close and much better than IWC. Moreover, the HRWA is five to twenty times faster to compute than other methods, depending on the mesh size. Second, an experimental case is presented where bending and torsion waves are identified, yielding an apparent viscoelastic Young and shear moduli on a wide-frequency range.