Modal resonance analysis of acoustic transmission and reflection losses in viscoelastic plates

Abstract

Transmission and reflection losses (TL, RL) are calculated as functions of frequency thickness (F×D) and incidence angle (ϑ) for single and multiple viscoelastic plates (steel, ABS, syntactic foam, neoprene, and Plexiglas) using a transfer matrix method modified to include complex wave velocities. The calculation of these velocities depends on four measurable material constants: longitudinal and shear phase velocities (cL, cs) and absorption coefficients (αL, αS). A physical model is developed to relate αL to αS, and shown to be experimentally accurate for a wide range of materials, temperatures and frequencies, thus providing a new way to account for shear absorption when directly measured data is not readily available. Use of actual measured data is shown to be necessary to validly compare theory with the experimentally observed TL and RL. Analysis of maxima and minima in TL, RL versus F×D or ϑ is made in detail using calculated dispersion curves for single plates, and these extrema are shown to be consistant with the coincidence rule. In the case of a plate with high loss, the maxima in TL versus F×D, e.g., observed where minima would be expected from the coincidence rule, are explained in terms of interfering ’’resonance’’ peaks using a recent theory of acoustic resonances in plates. The concept of interfering resonances is shown to be successful in interpreting some of the previously unexplained features of TL and RL observed in steel.