Numerical research on dynamic stress of phononic crystal ROD in longitudinal wave band gap

Abstract

For the propagation of harmonic longitudinal stress wave in phononic crystal rod (PCR), transfer matrix of elastic wave in PCR was derived based on the wave equation and band structure of infinite PCR was calculated. For semi-infinite PCR, theoretical derivation of dynamic stress solutions of arbitrary section and internal interfaces was conducted with Bloch theorem. Inherent relationship between dynamic stress and surface wave modal frequency (SWMF) was analyzed. Afterwards, numerical computation mainly focusing on dynamic stress level of the internal interfaces of PCR was given in detail. Finally, numerical analysis for finite PCR was carried out and verified by finite element simulation. Our results show that SWMF has a significant influence on the dynamic stress, and exactly it is the formal pole of stress solution whose nature is directly determined by the sort order of the two materials constituting the PCR.