Guided modes in an elastic rectangular bar: solution based on partial plate mode decomposition

Similar to Auld's solution for Lamb waves, the wave modes in elastic rectangular bar are solved by partial wave decomposition method. The partial waves are composed of plate modes with the same wavenumber component in waveguide longitudinal direction, thus free boundary conditions on one pair of opposite surfaces are automatically satisfied. Based on completeness assumption and orthogonality of the plate modes, four independent eigen-equations are eventually derived for dispersion curve and mode shape investigation. Numerical evaluation shows the calculated results are in consistent with the FEM results. It is then verified that the plate modes which obliquely bounced back and forth between the two opposite surfaces compose the guided modes traveling in the rectangular waveguides.