ASYMPTOTIC ANALYSIS OF ACOUSTIC GREEN’S FUNCTIONS

Abstract

An asymptotic expansion of layered Green’s function is examination in a spatial domain and parametric approach is proposed by determining a small parameter to derive the shortened form of Green’s function for 3- and 4-layered structures. For qualitative testing and comparison of the exact Green’s function and asymptotic shortened Green’s functions associated with the measurement and source point in the same layer, we performed numerical calculations.

Keywords

• Green’s function
• layered media
• parametric analysis
• asymptotic approach

References

1. [1] Uzun B, Yücel H. An inverse source problem connected with thermoacoustic imaging in multi-layer planar medium. Journal of Mathematical Imaging and Vision 61 (2019): 874-884
2. [2] Xu M, Wang LV. Universal back-projection algorithm for photoacoustic computed tomography. Physical Review E, 2005, 71(1), 016706.
3. [3] Schoonover RW, Anastasio MA. Image reconstruction in photoacoustic tomography involving layered acoustic media. JOSA A, 2011, 28(6), 1114-1120.
4. [4] DiNapoli FR, Deavenport RL. Theoretical and numerical Green’s function field solution in a plane multilayered medium. The Journal of the Acoustical Society of America,1980, 67(1), 92-105.
5. [5] Dural G, Aksun MI. Closed-form Green's functions for general sources and stratified media. IEEE transactions on microwave theory and techniques, 43(7),1995, 1545-1552.
6. [6] Kaplunov J, Prikazchikov D, Sergushova O. Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods. Journal of Sound and Vibration, 2016,366, 264-276.
7. [7] Kaplunov YD, Prikazchikova LAE. Low-frequency vibration modes of strongly inhomogeneous elastic laminates. Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика, 2018, 18(4), 447-457.
8. [8] Özdemir Ö,Yücel H, Uçar YE, Erbaş B, Ege N. Green's functions for a layered high-contrast acoustic media. The Journal of the Acoustical Society of America, 2022, 151(6), 3676-3684.

9. [9] Prikazchikova L, Aydın YE, Erbaş B, Kaplunov J. Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate. Mathematics and Mechanics of Solids, 2020, 25(1), 3-16.