Natural property and vibration suppression of fluid-conveying phononic crystal pipes with axial periodic composites based on Timoshenko beam model

Phononic crystal (PC) structures have been applied in various engineerings since their vibration can be suppressed efficiently by the periodicity of the physical and geometrical properties. Inspired by this idea, in this paper, the free vibration and band gap (BG) characteristics of a fluid-conveying PC pipe composed of periodically varying materials are explored. The dispersion equation of the periodic pipe conveying fluid is established based on the Timoshenko beam model. By applying the spectral element method (SEM) in conjunction with the finite element method (FEM), the natural frequencies and vibration modes of the pipe are obtained, and the BG regions and vibration attenuation shapes are further achieved. The Euler–Bernoulli (E–B) beam model is also introduced for comparison. Comprehensive parametric studies are conducted. It is found that different BG location and width are presented for the Timoshenko and E-B pipe models. The number, physical and geometrical properties of the substructures and the fluid–structure interaction all have significant effects on the natural frequency, mode shape and BG performance of the PC pipe. In addition, as compared with the traditional transfer matrix method and FEM, the SEM is demonstrated a more efficient procedure to deal with not only the BG characteristics, but also natural properties of the PC dynamical structures.