H.L. Dai

Theoretical modeling and nonlinear analysis of piezoelectric energy harvesting from vortex-induced vibrations

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 and validated with experimental results. A reduced-order model is derived by using the Euler–Lagrange principle and implementing the Galerkin discretization. A van der Pol wake oscillator is used to model the vortex-induced lift force. A nonlinear analysis is performed to determine the required number of modes in the Galerkin discretization. It is demonstrated that a one- or two-mode approximation in the Galerkin approach is not sufficient to evaluate the performance of the harvester. Based on a five-mode approximation in the Galerkin approach, an identification for the van der Pol wake oscillator coefficients is performed. 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.

Modeling and performance of electromagnetic energy harvesting from galloping oscillations

The modeling and performance of a galloping-based electromagnetic energy harvester are investigated. To convert galloping oscillations into electrical energy, an electromagnetic transducer is used. A set of representative coupled equations that account for the transverse displacement of the bluff body and the induced electromagnetic current are constructed. The galloping force is modeled by using the quasi-steady approximation. The effects of the electrical load resistance on the coupled damping and onset speed of galloping are determined through a linear analysis. It is shown that the electrical load resistance strongly affects the coupled damping and hence the onset speed of galloping of the harvester. For high values of the electrical load resistance, it is demonstrated that the load resistance has a negligible impact on the onset speed of galloping. A nonlinear analysis is then performed to investigate the effects of the electrical load resistance and wind speed on the harvesters outputs. The nonlinear normal form is first derived and validated with numerical predictions in order to characterize the type of instability for various cross-section geometries. The results show that a very good agreement is obtained between the normal form solutions and numerical predictions near Hopf bifurcation. It is also shown that, for well-defined values of wind speeds, both the transverse displacement amplitude and the generated voltage are increasing with the electrical load resistance. On the other hand, there is an optimum value of the electrical load resistance, which varies with the wind speed, at which the levels of the harvested power are maximized.

Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method

Abstract The application of transfer matrix method (TMM) to the vibration analysis of three-dimensional (3D) pipelines conveying fluid is performed in this paper. Based on the equations of motion, in which the steady combined force is essentially included, a 3D straight pipe element and a curved pipe element conveying fluid are formulated by introducing dynamic stiffness matrix in order to apply the TMM. The natural frequencies of simple pipe systems with straight or circular shape are calculated to demonstrate the validity of the proposed treatment. Using TMM, the natural frequencies, frequency response functions and instability of 3D-shaped pipeline systems are analyzed, representing some fresh results. It is shown that, in the application of TMM to the vibration analysis of curved or 3D pipelines conveying fluid, the steady combined force has to be included, otherwise the obtained results may be not reliable.

Improving the performance of aeroelastic energy harvesters by an interference cylinder

An interference circular cylinder is introduced and placed downstream of the original circular cylinder for improving the output performance of energy harvesting from vortex-induced vibrations. The interference cylinder is fixed, but its spacing distance from the original cylinder can be adjusted. The experimental results show that the harvested power can be greatly enhanced and the bandwidth of the resonance region is also increased depending on the spacing distance and wind speed, compared to the original energy harvester without an interference cylinder. This is attributed to the fact that the flow pattern for the two cylinders changes with varying the spacing distance, resulting in distinctive characteristics of the Strouhal number and coefficients of fluctuating lift force and mean drag force. The present study gives a suggestive guidance in effectively harvesting energy from vortex-induced vibrations by adjusting the spacing distance according to the available wind speed.

Nonconservative pipes conveying fluid: evolution of mode shapes with increasing flow velocity

When the velocity of fluid flow in a cantilevered pipe is successively increased, the vibration characteristics of the system may vary remarkably. This paper is concerned with exploring the evolution of the actual mode shapes of the pipe with increasing flow velocity. Results show that the mode shapes of the cantilevered system may dramatically change due to the increment of flow velocity. At higher flow velocity, these mode shapes, indeed, differ much from those of the classical cantilevered beam. When a critical mass ratio at which the so-called ‘mode exchange’ phenomenon occurs was chosen, the corresponding two modes of the cantilevered pipe would have the same shape. In addition, the nonlinear responses of the system have also been linked to the lowest three mode shapes by comparing the calculated mode shapes with the limit-cycle motions obtained experimentally.