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This paper proposes and investigates a piezoelectric energy harvesting system based on the flow induced vibration of a piezoelectric composite cantilever pipe. Dynamic equations for the proposed energy harvester are derived considering the fluid-structure interaction and piezoelectric coupling vibration. Linear global stability analysis of the fluid-solid-electric coupled system is done using the numerical continuation method to find the neutrally stable vibration mode of the system. A measure of the energy harvesting efficiency of the system is proposed and analyzed. A series of simulations are conducted to throw light upon the influences of mass ratio, dimensionless electromechanical coupling, and dimensionless connected resistance upon the critical reduced velocity and the normalized energy harvesting efficiency. The results provide useful guidelines for the practical design of piezoelectric energy harvester based on fluid structure interaction and indicate some future topics to be investigated to optimize the device performance.