Reverberation-Ray Matrix Analysis and Interpretation of Bending Waves in Bi-Coupled Periodic Multi-Component Beams

Most existing research on periodic beams concerns bending waves in mono-coupled and bi-coupled periodic mono-component beams with the unit cell containing only one beam segment, and very few works on bi-coupled periodic multi-component beams with the unit cell containing more than one beam segments study the bending waves in structures with only binary unit cells. This paper presents the method of reverberation-ray matrix (MRRM) as an alternative theoretical method for analyzing the dispersion characteristics of bending waves with the wavelength greater than the size of the cross-sections of all components in bi-coupled periodic multi-component beams. The formulation of MRRM is proposed in detail with its numerically well-conditioned property being emphasized, which is validated through comparison of the results obtained with the counterpart results by other methods for exemplified bi-coupled periodic beams. Numerical examples are also provided to illustrate the comprehensive dispersion curves represented as the relations between any two among three in frequency, wavenumber (wavelength) and phase-velocity for summarizing the general features of the dispersion characteristics of bending waves in bi-coupled periodic multi-component beams. The effects of the geometrical and material parameters of constituent beams and the unit-cell configuration on the band structures are also demonstrated by numerical examples. The most innovative finding indicated from the dispersion curves is that the frequencies corresponding to the Brillouin zone boundary may not be the demarcation between the pass-band and stop-band for bending waves in bi-coupled periodic multi-component beams.