Characterization of a lossy elastic plate thanks to the relationships between its reflection and transmission coefficients.

Abstract

The normal reflection and transmission coefficients of a lossy elastic plate are measured and associated according to the outcomes of resonance scattering theory (RST) and S-matrix theory (SMT). The sum and the difference of those coefficients provide valuable tools, the transition terms, we use to characterize the plate. The absorption in the plate can be expressed via different manners recalled in the following. By means of a dimensionless loss factor, the velocities of the longitudinal and transverse waves of the studied aluminum plate are no more real but complex. The width of a resonance is the sum of two parts: the elastic width and the absorption one. In the vicinity of a resonance frequency, the transition terms obey the Breit–Wigner resonant form which makes it possible an easy determination of the two parts of the resonant width. There is a good experiment/theory agreement when an imaginary part is added to the Lamé coefficients of the aluminum plate. The loss factor is of the order 5.10–4. On the whole, the effect of the attenuation rises with frequency and reaches a maximal importance at the vicinity of a resonance frequency.