  This paper discusses the free vibration of elastic spherical structures in
the presence of an externally unbounded acoustic medium. In this vibration,
damping associated with the radiation of energy from the confined solid medium
to the surrounding acoustic medium is observed. Evaluating the coupled system
response (solid displacement and acoustic pressure) and characterizing the
acoustic radiation damping in conjunction with the media properties are the
main objectives of this research. In this work, acoustic damping is
demonstrated for two problems: the thin spherical shell and the solid sphere.
The mathematical approach followed in solving these coupled problems is based
on the Laplace transform method. The linear under-damped harmonic oscillator is
the reference model for damping estimation. The damping evaluation is performed
in frequency as well as in time domains; both investigations lead to identical
damping factor expressions.
