Nonlinear dynamics of energy harvesting system for cantilevered fluid-conveying pipes with stopper

To achieve self-powered sensing when complex dynamics exist in fluid-conveying pipes, a novel piezoelectric energy harvesting configuration of cantilevered fluid-conveying pipes with an integrated stopper is proposed to investigate nonlinear dynamics, and elucidate the dynamic mechanism to enhance the energy harvesting performance. The nonlinear governing equation of this configuration was established by applying Hamilton’s principle, and a set of ordinary differential equations was obtained using the Galerkin method. Considering the influence of a piezoelectric layer, the mode shapes with various orders of this configuration were determined by adopting the differential quadrature method. The harmonic balance method combined with the pseudo-arc length extension method was used to track the frequency responses, and the effectiveness of these responses was confirmed by comparing the analytical solutions to the numerical solutions obtained by the Runge–Kutta method. The global bifurcation diagrams, along with the phase trajectories, power spectra, and Poincaré maps, are presented to predict complex nonlinear dynamic behaviors, such as the coexistence of the system’s periodic motion and chaotic motion. The results reveal that the impact force nonlinearity caused by the stopper can effectively improve the energy harvesting efficiency and make the dynamic behavior exhibit softening or hardening characteristics. Parametric investigations were conducted for the flow velocity, resistance, stiffness, and stopper position. The numerical examples reveal that the proposed system plays an important role in vibration suppression and energy harvesting.