Reverberation-ray analysis of dispersion of elastic waves in a box-girder

Based on the classical plate theory and plane stress assumption, this paper calculates the dispersion curves of elastic waves in a box girder using the reverberation-ray matrix method. By dividing a box girder into several thin plates, the governing equations for each plate are given, and the transient wave solutions for a plate with infinite length are derived under dual local coordinate systems. Considering the balance conditions of forces and continuity conditions of displacements at every intersection, the local and global scattering relations can be obtained. Combining with the phase equation which is deduced from the intrinsic relation for the dual local coordinates, the reverberation-ray matrix is finally constructed and the characteristic equation for waves propagating in a box girder is obtained. In the numerical examples, the dispersion curves for a rectangular box girder are calculated. Due to the uniform formulations as well as numerical stability in calculation, the reverberation-ray matrix method is suitable for analyzing folded plate structures with arbitrary cross sections.