Analysis and Interpretation of Longitudinal Waves in Periodic Multiphase Rods Using the Method of Reverberation Ray Matrix Combined With the Floquet Bloch Theorem

Abstract

The method of reverberationray matrix (MRRM) combined with the Floquet–Bloch theorem, which serves as an alternative method, is presented for accurately analyzing longitudinal waves in general periodic multiphase rods. Closedform dispersion relation of periodic quaternary rods is derived. Based on this relation, the functions of constituentrod parameters in the formation of longitudinalwave band structures are analytically revealed. Numerical examples validate the proposed method and indicate the characteristics/applications of all kinds of dispersion curves that include the frequencywave number spectra, the frequencywavelength spectra, the frequencyphase velocity spectra, the wave numberphase velocity spectra and the wavelengthphase velocity spectra. The effect of unitcell layout on the frequency band properties and the functions of constituentrod parameters in the band structure formation are also illustrated numerically. The analysis and interpretation of longitudinal waves in periodic multiphase rods given in this paper will push forward the design of periodic structures for longitudinal wave filtering/guiding and vibration isolation/control applications.