Nonlinear behaviors and chaos control of a fluid-conveying piezoelectric pipe in supercritical regime

Abstract

The study investigated the steady state response of a piezoelectric pipe conveying fluid under external and internal resonances in the supercritical regime of fluid velocity. Internal resonance conditions between the first and second frequency modes were studied at a specific flow velocity in the supercritical regime. The Galerkin method and the multiple scale method were used to extract the vibration amplitude versus the excitation frequency and amplitude. The steady state solutions lost stability through saddle-node and Hopf bifurcations, leading to periodic, double periodic, multi-periodic, and chaotic behaviors in the forced and frequency response curves. Time response, FFT, phase portrait, and Lyapunov exponents were presented to predict the unstable regions of the piezo-pipe system between the Hopf points. The Wolf algorithm was utilized to evaluate the Lyapunov exponents. Additionally, a fuzzy terminal sliding mode controller was designed in the chaotic region of the piezoelectric pipe conveying fluid, and its parameters were optimized using the genetic algorithm. The controller effectively stabilized the chaotic motion of the system, demonstrating better performance than the sliding mode control in numerical results.