Bi-dimensional Finite Element Analysis of Linear and Circular Cylindrical Acoustic Waveguides
|關鍵字:||雙維有限元素;波導;楔型體;Bi-dimensional Finite Element;Waveguides;Wedge|
A bi-dimensional finite element model based on Hamilton’s principle and finite element method is developed in this thesis to analyze the dispersive characteristics and mode shapes of normal modes for linear and circular cylindrical 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 code, ANSYS ver.5.7. The convergence was simultaneously discussed. The 3D FEA has limitation in calculation for higher normal modes due to constraint in the available number of elements. The bi-dimensional finite element method is based on separation of variables, in which the wave propagation factor is separated from cross-sectional vibrations of the acoustic waveguides. The present method has advantages in determination of phase velocities and mode shapes up to higher normal modes and in a wide range of frequencies without loss of accuracy. Phase velocities of the antisymmetric flexural (ASF) guided waves in linear-wedge waveguides are found to be slower than the Rayleigh wave speed. The calculated results in the range of higher wave numbers are in a good agreement with the empirical formula provided by Lagasse. The ASF waves in either linear or circular cylindrical wedge-typed waveguides have faster and frequency-dependent phase velocities in the range of lower wave numbers. It 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, curvatures of the acoustic waveguides increase the phase velocities of higher normal modes only. Contrary to the wedge-typed waveguides, the guided wave propagation in both linear and circular rectangular waveguides is dispersive. Most energy carried by the ASF waves in the wedge-typed waveguides is confined at the tip of wedge and is observed in the corresponding mode shapes. However, wave motion for the rectangular waveguides spreads over whole cross section. The evidence indicates that other kinds of normal modes such as extensional waves appear in the rectangular waveguides.