A nonlinear inerter pendulum vibration absorber is integrated with an electromagnetic power take-off system (called IPVA-PTO) and is analyzed for its efficacy in ocean wave energy conversion of a spar platform. The IPVA-PTO system shows a nonlinear energy transfer phenomenon between the spar and the IPVA-PTO which can be used to convert the vibration energy of the spar into electricity while reducing the hydrodynamic response of the spar. The hydrodynamic coefficients of the spar are computed using a commercial boundary-element-method (BEM) code. It is shown that the energy transfer is associated with 1:2 internal resonance of the pendulum vibration absorber, which is induced by a period-doubling bifurcation. The period-doubling bifurcation is studied using the harmonic balance method. A modified alternating frequency/time (AFT) approach is developed to compute the Jacobian matrix involving nonlinear inertial effects of the IPVA-PTO system. It is shown that the period-doubling bifurcation leads to 1:2 internal resonance and plays a major role in the energy transfer between the spar and the pendulum. The response amplitude operator (RAO) in heave and the capture width of the IPVA-PTO-integrated spar are compared with its linear counterpart and it is shown that the IPVA-PTO system outperforms the linear energy harvester as the former has a lower RAO and higher capture width.
This content will become publicly available on October 1, 2024
The inerter pendulum vibration absorber (IPVA) is integrated between a spar and an annulus floater using a ball-screw mechanism to study its wave energy conversion potential. Hydrodynamic stiffness, added mass, and radiation damping effects on the spar-floater system are characterized using the boundary element method. It is found that a 1:2 internal resonance via a period-doubling bifurcation in the system is responsible for nonlinear energy transfer between the spar-floater system and the pendulum vibration absorber. This nonlinear energy transfer occurs when the primary harmonic solution of the system becomes unstable due to the 1:2 internal resonance phenomenon. The focus of this paper is to analyze this 1:2 internal resonance phenomenon near the first natural frequency of the system. The IPVA system when integrated with the spar-floater system is shown to outperform a linear coupling between the spar and the floater both in terms of the response amplitude operator (RAO) of the spar and one measure of the energy conversion potential of the system. Finally, experiments are performed on the IPVA system integrated with single-degree-of-freedom system (without any hydrodynamic effects) to observe the 1:2 internal resonance phenomenon and the nonlinear energy transfer between the primary mass and the pendulum vibration absorber. It is shown experimentally that the IPVA system outperforms a linear benchmark in terms of vibration suppression due to the energy transfer phenomenon.
more » « less- Award ID(s):
- 2127495
- NSF-PAR ID:
- 10467700
- Publisher / Repository:
- American Society of Mechanical Engineers
- Date Published:
- Journal Name:
- Journal of Vibration and Acoustics
- Volume:
- 145
- Issue:
- 5
- ISSN:
- 1048-9002
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract -
A nonlinear inerter pendulum vibration absorber is integrated with an electromagnetic power take-off system (called IPVA-PTO) and is analyzed for its efficacy in ocean wave energy conversion of a spar platform. The IPVA-PTO system shows a nonlinear energy transfer phenomenon between the spar and the IPVA-PTO which can be used to convert the vibration energy of the spar into electricity while reducing the hydrodynamic response of the spar. The hydrodynamic coefficients of the spar are computed using a commercial boundary-element-method (BEM) code. It is shown that the energy transfer is associated with 1:2 internal resonance of the pendulum vibration absorber, which is induced by a period-doubling bifurcation. The period-doubling bifurcation is studied using the harmonic balance method. A modified alternating frequency/time (AFT) approach is developed to compute the Jacobian matrix involving nonlinear inertial effects of the IPVA-PTO system. It is shown that the period doubling bifurcation leads to 1:2 internal resonance and plays a major role in the energy transfer between the spar and the pendulum. The response amplitude operator (RAO) in heave and the capture width of the IPVA-PTO-integrated spar are compared with its linear counterpart and it is shown that the IPVA-PTO system outperforms the linear energy harvester as the former has a lower RAO and higher capture width.more » « less
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Abstract The inerter has been integrated into various vibration mitigation devices, whose mass amplification effect could enhance the suppression capabilities of these devices. In the current study, the inerter is integrated with a pendulum vibration absorber, referred to as inerter pendulum vibration absorber (IPVA). To demonstrate its efficacy, the IPVA is integrated with a linear, harmonically forced oscillator seeking vibration mitigation. A theoretical investigation is conducted to understand the nonlinear response of the IPVA. It is shown that the IPVA operates based on a nonlinear energy transfer phenomenon wherein the energy of the linear oscillator transfers to the pendulum vibration absorber as a result of parametric resonance of the pendulum. The parametric instability is predicted by the harmonic balance method along with the Floquet theory. A perturbation analysis shows that a pitchfork bifurcation and period doubling bifurcation are necessary and sufficient conditions for the parametric resonance to occur. An arc-length continuation scheme is used to predict the boundary of parametric instability in the parameter space and verify the perturbation analysis. The effects of various system parameters on the parametric instability are examined. Finally, the IPVA is compared with a linear benchmark and an autoparametric vibration absorber and shows more efficacious vibration suppression.more » « less
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