Simple low‐frequency model for response of compliant coatings

Abstract

Given is a thin, compliant coating, perfectly bonded to a rigid base. It is desired to find the impedance of the coating at its free surface with respect to two‐dimensional, harmonic waves. In practical applications, the coating can serve as a flexible boundary that supports some action in the adjoining medium, i.e., acoustic waves or waves in fluid flow. The exact continuum model of the coating is that of viscoelasticity [M. Pierucci, J. Acoust. Soc. Am. 61, 965–971 (1977); M. Gad‐el‐Hak et al., J. Fluid Mech. 140, 257–280 (1984)]. In many applications, the solution in the adjoining medium is very complicated, and the evaluation of the surface impedance must be carried out many times. Sometimes an oversimplified replacement of the coating is used, such as that of a membrane [T. B. Benjamin, J. Fluid Mech. 9, 513–532 (1960)], which has response characteristics completely different from those that are given by the surface impedance of the coating. The objective of this paper is to show that a simple one‐degree‐of‐freedom model can be constructed, as simple as that of the membrane, which still retains the main response characteristics of a solid coating, or of a stack of composite coatings. This simple model is valid for cases in which the response is dominated by the lowest frequency mode of the coating. Detailed results are given for the determination of the parameters of the model. As an example, the fluid‐solid interaction problem, considered by Gad‐el‐Hak et al., is solved and shown that the results of the simple model and those of viscoelasticity are almost the same. [This was supported by ONR Grant N00014‐81‐0398.]