Damping Evaluation for Free Vibration of Spherical Structures in Elastodynamic-Acoustic Interaction

TL;DR

This paper investigates the damping effects in free vibrations of spherical elastic structures interacting with an unbounded acoustic medium, using Laplace transform methods to evaluate energy radiation damping.

Contribution

It introduces a mathematical approach to evaluate acoustic radiation damping in spherical structures, applicable to both thin shells and solid spheres, in frequency and time domains.

Findings

Damping expressions are consistent in both frequency and time analyses.

Acoustic damping is demonstrated for spherical shells and solid spheres.

The approach provides a quantitative measure of energy radiation damping.

Abstract

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.