Dynamics of a thin elastic coating

Forced vibrations of a thin elastic coating are considered. A long wave, multimode approximation is derived from the original 3D setup. It is governed by a 2D equation with the coefficients depending on trigonometric functions of the frequency parameter. The related explicit dispersion relations appear to be of general interest as well. Although the developed asymptotic formulation is oriented to the analysis of the effect of normal stresses slowly varying along the upper face of the coating, it is also useful for evaluating the majority of the resonance responses due to delta-type loading. Numerical comparisons between exact and asymptotic predictions are presented.