Wave Propagation in Flexible Tubes Immersed in Fluid
Date Issued
2016
Date
2016
Author(s)
Tu, Ya-Chi
Abstract
The wave propagation in flexible tubes immersed in fluid is studied in order to explore the effect of ultrasonic waves incident on blood vessels. Based on Chebyshev-Gauss-Lobatto interpolation and differential matrix, spectral method discretizes the Helmholtz equation to establish generalized eigenvalue problems. These generalized eigenvalue problems are formulated for axial symmetric, circumferential, and bending modes respectively. The numerical method overcomes the divergent problem of Bessel functions and the spectrum, mode shapes, and motion of particles are found successfully. Mode shapes corresponding to the first and second dispersion curves display surface wave patterns of the tube in a very wide frequency range. The first dispersion curve gives antisymmetric modes while the second one offers symmetric modes. Before convergence, the third and fourth dispersion curves provide interface waves of fluid on both inside and outside of tubes. As frequency is increased, mode shapes corresponding to the third dispersion curve converge to surface waves of fluid outside the tube and that corresponding to the fourth dispersion curve converge to surface waves of fluid inside the tube. For EKOS operated at high frequency mode of 2MHz, surface wave modes will be excited most due to the ultrasonic source location. Therefore, the ultrasonic energy is mainly concentrated in the vicinity of vessel surface. When it is operated at low frequency mode of 45kHz, there is more ultrasonic energy penetrating into the vessel wall than that of 2MHz mode. That is, high frequency operation mode causes less damage to the vessel than low frequency operation mode.
Subjects
Flexible tube
Blood vessel
Ultrasonic wave
Dispersion curve
Mode shape
Type
thesis