Vibration Mode Analyses for Circular Wedge Acoustic Waveguides

A bi-dimensional finite element model based on Hamilton's principle and the finite element method is developed in this study to analyze the dispersive characteristics and mode shapes of normal modes for circular wedge acoustic waveguides. The dispersion curves of phase velocities for guided waves and their corresponding resonant frequencies for a circular wedge waveguide were also evaluated by 3D finite element analysis (FEA) using the commercial ANSYS code. The convergence of guided waves was discussed. The 3D FEA was limited in terms of calculating for higher normal modes due to constraints in the available number of elements. The bi-dimensional finite element method is based on the separation of variables, with the wave propagation factor being separated from cross-sectional vibrations of the acoustic waveguides. The present method has advantages in terms of being able to determine phase velocities and mode shapes up to higher normal modes and in a wide range of frequencies without loss of accuracy. The phase velocities of the anti-symmetric flexural (ASF) guided waves in circular wedge waveguides were found to be slower than the Rayleigh wave speed. Furthermore, the calculated results in the range of higher wave numbers were in good agreement with the empirical formula provided by Lagasse [1]. The ASF waves in circular cylindrical wedge-typed waveguides were found to have faster and frequency-dependent phase velocities in the range of lower wave numbers. This phenomenon results from the boundary conditions on the bottom of waveguides, which are different from the ideal wedge problem considered in Lagasse's work. In addition, the curvatures of the acoustic waveguides were found to increase the phase velocities of higher normal modes only.