This paper investigates the flexural wave propagation and control of a novel piezoelectric composite pipe conveying fluid. Dual piezoelectric layers, used as sensors and actuators, are periodically arranged on the pipe, with a feedback amplifying circuit connecting them to form a self-powered phononic crystal (PC) control structure. The vibration reduction performance can be actively tuned by adjusting the feedback control gain, rather than modifying the pipe's construction. The pipe is composed of functionally graded material (FGM), with material properties varying continuously along the radial direction, and a poroelastic medium is introduced. Using the Timoshenko beam theory and Hamilton's principle, electromechanical coupling equations governing flexural vibration are derived. The band structure, band gap (BG) distribution, and frequency response are analyzed using spectral element technology. Parametric studies show that the proposed design effectively controls vibrations, with significant impacts from material properties, piezoelectric layers, feedback control, and flowing fluid on BG characteristics. This work provides a technological reference for vibration and elastic wave control in engineering composite pipe structures. The paper reviews recent research on phononic crystals (PCs) and acoustic metamaterials (AMs) for vibration and noise reduction. It discusses the integration of PCs and piezoelectric structures for vibration isolation and acoustic attenuation. The study also explores the use of piezoelectric materials in vibration control, including the transfer matrix method (TMM), plane wave expansion method (PWEM), and finite element method (FEM). The spectral element method (SEM) is adopted for its accuracy and convergence. Functionally graded materials (FGMs) are superior composite materials with non-uniform properties. They are used in engineering pipes conveying fluid, but few studies consider vibration suppression and wave motion characteristics of FGM pipes. The paper proposes a novel PC model of FGM poroelastic pipe with periodic piezoelectric layers. Dual piezoelectric layers are periodically arranged on the pipe, with a voltage feedback circuit forming a self-powered PC control structure. The Timoshenko beam theory is used for modeling, and the electromechanical governing equations of flexural vibration are derived. The band structure, BG distribution, and frequency response are analyzed using SEM. The impacts of material, piezoelectric layers, feedback control, and flowing fluid on BG characteristics are discussed. The elastic wave shapes of the pipe are exhibited to visualize the vibration control effect.This paper investigates the flexural wave propagation and control of a novel piezoelectric composite pipe conveying fluid. Dual piezoelectric layers, used as sensors and actuators, are periodically arranged on the pipe, with a feedback amplifying circuit connecting them to form a self-powered phononic crystal (PC) control structure. The vibration reduction performance can be actively tuned by adjusting the feedback control gain, rather than modifying the pipe's construction. The pipe is composed of functionally graded material (FGM), with material properties varying continuously along the radial direction, and a poroelastic medium is introduced. Using the Timoshenko beam theory and Hamilton's principle, electromechanical coupling equations governing flexural vibration are derived. The band structure, band gap (BG) distribution, and frequency response are analyzed using spectral element technology. Parametric studies show that the proposed design effectively controls vibrations, with significant impacts from material properties, piezoelectric layers, feedback control, and flowing fluid on BG characteristics. This work provides a technological reference for vibration and elastic wave control in engineering composite pipe structures. The paper reviews recent research on phononic crystals (PCs) and acoustic metamaterials (AMs) for vibration and noise reduction. It discusses the integration of PCs and piezoelectric structures for vibration isolation and acoustic attenuation. The study also explores the use of piezoelectric materials in vibration control, including the transfer matrix method (TMM), plane wave expansion method (PWEM), and finite element method (FEM). The spectral element method (SEM) is adopted for its accuracy and convergence. Functionally graded materials (FGMs) are superior composite materials with non-uniform properties. They are used in engineering pipes conveying fluid, but few studies consider vibration suppression and wave motion characteristics of FGM pipes. The paper proposes a novel PC model of FGM poroelastic pipe with periodic piezoelectric layers. Dual piezoelectric layers are periodically arranged on the pipe, with a voltage feedback circuit forming a self-powered PC control structure. The Timoshenko beam theory is used for modeling, and the electromechanical governing equations of flexural vibration are derived. The band structure, BG distribution, and frequency response are analyzed using SEM. The impacts of material, piezoelectric layers, feedback control, and flowing fluid on BG characteristics are discussed. The elastic wave shapes of the pipe are exhibited to visualize the vibration control effect.