Flow-induced Vibrations Of Slender Structures And Their Applications In Energy Harvesting

Flow-induced vibrations of pipes, beams and circular cylinders and their potential applications in energy harvesting are investigated in this thesis. Firstly, the dynamics of the pipe subjected to axial internal fluid is explored, then we propose a passive control method to enhance the stability of pipes conveying fluid. Secondly, vortex-induced vibrations (VIV) of fluid-conveying pipes are analyzed, and the effects of internal flow velocity being in the supercritical regime, fluctuating and base excitation parametric resonances on the nonlinear dynamics of pipes conveying fluid subjected to VIV are mainly discussed. Finally, based on the VIV mechanism, researches on energy harvesting from vortex-induced vibrations of a piezoelectric cantilever beam with a circular cylinder attached to its end are performed. In contrast to previous studies, the present study has main features as follows:1. The dynamics of hybrid pipes is further investigated by constructing models of fluid-conveying cantilevered pipes composed of two segments made of different materials.: The lowest and second critical flow velocities and modes for flutter instability are intensively analyzed. It is demonstrated that the critical flow velocity curves may contain S-and/or Z-shaped segments with varying length ratios between the two segments, and the flutter instability may first occur in the fourth mode, which is different from that reported before based on a uniform pipe conveying fluid.2. A passive control method is proposed to improve the vibration and stability properties of fluid-conveying pipes. The control method is validated theoretically for improving stabilities of cantilevered and pinned-pinned slender pipes. It is found that not only the critical flow velocity of the pipe system can be greatly increased, but also the vibration frequency of the fluid-conveying pipes can be comfortably controlled, as well as the potential usefulness for the design and improvement of engineering pipeline systems and fluidic devices.3. The dynamics of simply supported fluid-conveying pipes with geometric imperfections is examined, by considering the effects of four kinds of imperfections on stabilities of the pipe. Bases on four modes Galerkin procedure, the nonlinear equation is discretized. Linear analysis shows that each type of imperfections affects the natural frequency of only one single mode. For half-sinusoidal wave or parabolic variation of imperfections, the critical flow velocity at which buckling occurs is higher than that for a pipe without imperfections. Nonlinear analysis predicts that buckling displacement of the pipe may be asymmetric due to the presence of imperfections. Moreover, the nonlinear theory predicts a lower critical flow velocity than that predicted by the linear theory for pipes with half-sinusoidal wave or parabolic imperfections.4. The vortex-induced vibrations of pipes conveying fluid are examined, by considering the internal fluid velocities varying from the subcritical to the supercritical regions. Based on coupled system models, the nonlinear coupled equations of motion are constructed for pipes transporting subcritical or supercritical fluid flows. It is shown that when the internal fluid velocity is in the subcritical region, the pipe is always vibrating periodically and that with increasing external fluid reduced velocity the vibration amplitude of the pipe increases first and then decreases, with jumping phenomenon between the upper and lower response branches. When the internal fluid velocity is in the supercritical region, however, the pipe displays various dynamical behaviors around the post-buckling configuration such as periodic, period-doubling, inverse period-doubling bifurcations, and chaotic motions.5. The vortex-induced vibrations of a long flexible pipe conveying fluctuating flows are investigated. Base on the direct perturbation method of multiple scales (MMS), the dynamics of the pipe with principal parametric resonances during lock-in for each of the first two modes are analyzed numerically. The results indicate that in the case of a pipe containing fluctuating flows, the peak of vibration amplitudes is larger than that of a pipe conveying steady flows. With the increase of detuning parameter for the frequency of pulsating flow, the variation range of vibration amplitudes of the pipe enlarges first and then narrows, with jumping phenomenon that the vibration amplitude changes from multi-value to single-value and then returns to multi-value between the two regions of multi-value responses, which has not been discovered yet. Indeed, from the amplitude-frequency response curves one can see that the hysteresis may occur. Finally, the method of numerical simulations (MNS) is directly employed to verify the implementation of MMS.6. The extended Hamilton’s principle and the Galerkin procedure are used to investigate the nonlinear dynamical responses of a vertical riser concurrently subjected to hybrid excitations, namely, vortex-induced vibrations (VIVs) and base excitations. Linear and nonlinear analyses are performed to investigate the effects of internal fluid velocity, cross-flow speed, and base acceleration on the coupled frequency, onset speed of synchronization, and vibration amplitudes of the riser. The results show that when the cross-flow speed becomes in the synchronization region, vibration behaviors of the riser change from aperiodic to periodic motions, with a jumping phenomenon between these two kinds of motions. The results also show that an increase of the base acceleration results in a wider synchronization region and a significant effect associated with the quenching phenomenon.7. A nonlinear distributed-parameter model for harvesting energy from vortex-induced vibrations of a piezoelectric cantilever beam with a circular cylinder attached to its end is developed by using the Lagrange and virtual principle. The model is validated through experimental results. To design efficient piezoaeroelastic energy harvesters that can generate energy at low freestream velocities, further analysis is performed to investigate the effects of the cylinder’s tip mass, length of the piezoelectric sheet, and electrical load resistance on the synchronization region and performance of the harvester. The results show that, depending on the operating freestream velocity, the cylinder’s tip mass, length of the piezoelectric sheet, and electrical load resistance can be optimized to design enhanced piezoaeroelastic energy harvesters from vortex-induced vibrations.