An equivalent source method for acoustic problems with thermoviscous effects.

This paper presents an equivalent source method (ESM) for analyzing sound propagation in small-scale acoustic structures with thermoviscous effects. The formulations that describe the thermal, viscous, and acoustic modes for thermoviscous acoustic problems are introduced. The concept of ESM is then applied to solve these formulations, resulting in an efficient numerical computation and implementation procedure. Based on two different strategies, the obtained ESM formulations are coupled at the boundary using the isothermal, non-slip, and null-divergence conditions. The coupling based on the first strategy is efficient for solving thermoviscous acoustic problems with few matrices required. However, this procedure faces the evaluation of the tangential derivatives of the boundary velocity. Coupling the ESM formulations directly for each component of the total particle velocity at the boundary has no such problem, which leads to the second strategy. However, it entails a larger memory usage compared to the former. Additionally, the coupled finite element method (FEM)-ESM formulations based on the above strategies are developed for acoustic-structural interaction. The validity of the presented ESM formulations is demonstrated through benchmark examples, and that of the coupled FEM-ESM formulation is illustrated by the numerical analysis of a simplified microphone.

Analytical method for studying acoustic fields radiated by general spherical sound sources in thermoviscous fluids.

The study of acoustic radiation from spherical sound sources plays a crucial role in understanding the thermoviscous effects in practical acoustic problems. However, finding a general solution of acoustic radiation from spherical sound sources in thermoviscous fluids remains a formidable challenge. To advance this issue, an analytical method is developed in this paper to calculate the acoustic field radiated by spherical sound sources with the isothermal boundary condition and arbitrary velocity boundary condition. The developed method is utilized to present the solutions of the acoustic field generated by an oscillating sphere and a general spherical sound source, and the accuracy and validity of these solutions are verified through analytical and numerical methods.