Trapped modes in an infinite or semi-infinite tube with a local enlargement.
Trapped modes in a hard cylindrical tube with a local axisymmetric enlargement or bulge and filled with a uniform acoustic medium is studied. The governing Helmholtz equation in the cylindrical coordinate system is employed to deal with this problem through the domain decomposition method and matching technique. The trapped modes and the corresponding frequencies less than the threshold frequency or cut-off frequency are derived. It is found that in addition to the fundamental mode, the second- and higher-order trapped modes exist and depend on the geometry parameters of the local bulge. The effects of the bulge radius and width on the frequencies are discussed. The local bulge leads to a decrease of the frequencies and the corresponding vibration mode is localized near the bulge. A multimodal analysis is made and frequency band gap of generalized trapped modes is also studied. A frequency band gap depends on the radius of a bulge and is independent of its width. The obtained results can be extended to analyze bound states in quantum wires.
School of Civil Engineering, Central South University, Changsha 410075, PR China.
Wei-Sha
WS
Li
School of Civil Engineering, Central South University, Changsha 410075, PR China.
Jiaqi
J
Zou
State Key Laboratory of Structural Analysis for Industrial Equipment and Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, PR China.
Kang Yong
KY
Lee
School of Civil Engineering, Central South University, Changsha 410075, PR China; State Key Laboratory of Structural Analysis for Industrial Equipment and Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, PR China. Electronic address: xfli@csu.edu.cn.
Xian-Fang
XF
Li
Domain decomposition; Frequency band gap; Helmholtz equation; Local enlargement; Matching method; Trapped mode