Comments on ‘‘Sound radiation from finite cylindrical coated shells, by means of asymptotic expansion of three‐dimensional equations for coating’’ [J. Acoust. Soc. Am. 96, 277–286 (1994)

Abstract

The idea of expanding elastic variables in powers of a thickness coordinate is not new, having been employed by Bassett as early as 1890 [Philos. Trans. R. Soc. Ser. A 181, 433–480]. A variety of works over the past decade, which were heavily influenced by Mindlin [‘‘An Introduction to the Mathematical Theory of Vibrations of Elastic Plates,’’ A Monograph Prepared for U.S. Army Signal Corps Engineering Laboratories, Fort Monmouth, NJ (1955)], have established that such expansions should introduce readily identifiable approximations. McDaniel and Ginsberg [J. Acoust. Soc. Am. 90, 2341 (1991) and J. Appl. Mech. 60, 152–157 (1993)] successfully addressed this idea with displacement expansions used in conjunction with Hamilton’s principle. The resulting formulation avoids many of the assumptions and complications that appear in the recent asymptotic analysis by Laulagnet and Guyader [J. Acoust. Soc. Am. 96, 277–286 (1994)], including assumptions on thickness relative to radius and to characteristic wavelength...