Bandgap accuracy and characteristics of fluid-filled periodic pipelines utilizing precise parameters transfer matrix method

Abstract

The phononic crystal theory provides a novel approach for effectively controlling the bending vibrations in fluid-filled pipelines. This paper innovatively proposes the precise parameters transfer matrix method to investigate the band calculation accuracy and bandgap characteristics of fluid-filled periodic pipelines with various beam types. Firstly, the differential equations for bending vibration of fluid-filled pipelines are established based on deformation and force analysis. The parameters of the system state are precisely represented by the structural form of multiplying the constitutive matrix with the derivative matrix. Combined with Bloch's theorem, the novel precise parameters transfer matrix method for calculating the band structure is proposed. Secondly, the validity of this method is verified through a comparison with finite element simulation results. A detailed analysis is provided regarding the mechanism of bandgap formation and the effect of fluid filling on the band structure. Then, the influence of shear deformation, moment of inertia, and their coupling on the band calculation accuracy for fluid-filled periodic pipelines is studied based on various beam theories. Finally, it delves into the bandgap characteristics of fluid-filled periodic pipelines under different material parameters, structural parameters, and excitation conditions. This research offers valuable insights for the structural design and vibration damping application in fluid-filled periodic pipelines, providing theoretical support for accurately determining their bandgaps.