Frequency Bands Analysis Of The High-frequency Longitudinal Waves In Periodic Rods

Periodic structure is composed of same basic units which are in plane or in space connected in sequence in accordance with translational symmetry. In the periodic structure, there is a structure which periodic change elastic constants of its basic structural units. Such periodic structure is referred to phononic crystals. Phononic crystal material or structure with its excellent dynamic characteristics, excellent damping performance and in terms of noise suppression, has become an extraordinarily hot topic in dynamics and solid mechanics.When elastic waves propagate in the phononic crystal, because of the influence of the periodic change of the elastic constants, the elastic waves will be regularly scattered, thus, scattering waves will be formed in the phononic crystal. These scattering waves and incident waves constantly interfere, thus, the phononic crystal has a unique elastic wave band structure property, which can stagger frequency range into passband and band gap. When the elastic waves propagate in phononic crystal, within the pass-band frequency range elastic waves will be no attenuation, whereas the frequency of the wave within the stop band will be inhibited and cannot propagate.As the simplest phononic crystal structure, periodic rod structure also has a band characteristic. Selecting periodic rod structure as the object of study, not only reduces modes of the elastic waves and reduces the mode coupling and conversion of elastic waves, but also reduces the impact of locally resonant. Using periodic rod structure as the research object avoid the complexity of confounding factors, making research on the band structure of the cycle becomes convenient lever.However, current research on the method of simplified model on the rod is still too rough. Not only hasn’t a clear understanding of high frequency longitudinal wave propagation in periodic rods, but also lack of an exact calculation method which can give precise results at elastic waves within high frequency condition.In this paper, the method of reverberation-ray matrix (MRRM) combined with modified rod theories is presented for accurately high-frequency analyzing elastic waves in the periodic rod. Firstly, establish dynamic equations of modified rod theatrical model. And then combined with the analysis of periodic structures using Floquet principle establish scattering relationship. Then according to a unique dual-coordinate system of method of reverberation-ray matrix, we can get the phase relationship of structures. Finally, according to the scattering relationships and phase relationships, derive the rod dispersion equation. Solving the dispersion equation by a computer program, we can get characteristics and scope of application of several rod theories.Through the introduction of modified rod theory combined with the method of reverberation-ray matrix, making the high-frequency longitudinal wave propagation in periodic rods can be solved out more precise.This paper also obtained the several kinds of characteristics of dispersion curve of the different theorem by comparing; Finally by comparing several different phase dispersion curves under different rod theories, this article also gets several rod theories applicable scopes.