TY - JOUR
T1 - On the acoustic trapped modes and their symmetry properties in a circular cylindrical waveguide with a cavity
AU - Langthjem, Mikael A.
AU - Nakano, Masami
N1 - Funding Information:
We wish to thank Professor Nobumasa Sugimoto of Kansai University for comments which led to the present study. The major part of the work was carried out while the first author was affiliated with Faculty of Engineering, Yamagata University, Japan, and the second author was affiliated with Institute of Fluid Science, Tohoku University, Japan. Financial support by the Institute of Fluid Science, Tohoku University, via a ‘Collaborative Research Project’ (project code J17I030, to Yamagata University) is gratefully acknowledged.
Funding Information:
We wish to thank Professor Nobumasa Sugimoto of Kansai University for comments which led to the present study. The major part of the work was carried out while the first author was affiliated with Faculty of Engineering, Yamagata University, Japan, and the second author was affiliated with Institute of Fluid Science, Tohoku University, Japan. Financial support by the Institute of Fluid Science, Tohoku University, via a ‘Collaborative Research Project’ (project code J17I030, to Yamagata University) is gratefully acknowledged.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2021/6
Y1 - 2021/6
N2 - The paper is concerned with a partly analytical, partly numerical study of acoustic trapped modes in a cylindrical cavity (expansion chamber), placed in between two semi-infinite pipes acting as a waveguide. Trapped mode solutions are expressed in terms of Fourier–Bessel series, with the expansion coefficients determined from a determinant condition. The roots of the determinant, expressed in terms of the real wavenumber k, correspond to trapped modes. For a shallow cavity and for low values of the circumferential mode number it is found that there is just one trapped mode in the allowable wave number domain, and this mode is symmetric about a radial axis in the center of the cavity. As the circumferential mode number is increased, more and more trapped modes, placed between two cutoff frequencies, come into play, and they alternate between symmetric and antisymmetric modes. An analytical explanation of the mechanism behind the mode increasing and mode alternation is given via asymptotic expressions of the determinant condition. Numerical computations are done for verification of the analytical results and for consideration of less shallow cavities. Also for these cases, similar phenomena of an increasing number of trapped modes, and alternation between symmetric and antisymmetric modes, are found.
AB - The paper is concerned with a partly analytical, partly numerical study of acoustic trapped modes in a cylindrical cavity (expansion chamber), placed in between two semi-infinite pipes acting as a waveguide. Trapped mode solutions are expressed in terms of Fourier–Bessel series, with the expansion coefficients determined from a determinant condition. The roots of the determinant, expressed in terms of the real wavenumber k, correspond to trapped modes. For a shallow cavity and for low values of the circumferential mode number it is found that there is just one trapped mode in the allowable wave number domain, and this mode is symmetric about a radial axis in the center of the cavity. As the circumferential mode number is increased, more and more trapped modes, placed between two cutoff frequencies, come into play, and they alternate between symmetric and antisymmetric modes. An analytical explanation of the mechanism behind the mode increasing and mode alternation is given via asymptotic expressions of the determinant condition. Numerical computations are done for verification of the analytical results and for consideration of less shallow cavities. Also for these cases, similar phenomena of an increasing number of trapped modes, and alternation between symmetric and antisymmetric modes, are found.
KW - Acoustics
KW - Expansion chamber
KW - Localized modes
KW - Mode alternation
UR - http://www.scopus.com/inward/record.url?scp=85106719888&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85106719888&partnerID=8YFLogxK
U2 - 10.1007/s10665-021-10126-2
DO - 10.1007/s10665-021-10126-2
M3 - Article
AN - SCOPUS:85106719888
VL - 128
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
SN - 0022-0833
IS - 1
M1 - 14
ER -