Bandgap tuning and stress concentration reduction in fluid-filled periodic pipes via functionally graded materials

The stress concentration defect inevitably occurs at the interface of different materials or structures in the classical periodic pipe. This paper innovatively combines Phononic Crystals with functionally graded materials (FGM) to investigate the effects of introducing FGM on bandgap tuning and stress distribution in fluid-filled periodic pipes. Initially, a novel functionally graded (FG) unit cell is designed, accompanied by a theoretical model of a fluid-filled periodic pipe under external axial stress. Next, by integrating the finite element idea with traditional bandgap calculation methods, a hybrid strategy suitable for FG periodic structures is proposed. Then, the accuracy and applicability of the proposed strategy are validated through a comparison with the Element-spectral element method and Element-transfer matrix method. The effectiveness of stress concentration mitigation is highlighted through COMSOL simulation. Finally, a detailed discussion is provided on the effects of structural parameters, material properties, and external axial stress on the bandgap characteristics and stress distribution. This study not only provides solutions to the common problem of stress concentration in Phononic Crystals but also offers theoretical support for calculating the bandgap of periodic structures with continuously varying parameters.