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Abstract 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.
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On the Nonlinear Mode-Coupling in Ultra Precision Manufacturing Machines: Experimental and Analytical Analyses
Abstract Recent studies in passively-isolated systems have shown that mode coupling is desirable for best vibration suppression, thus refuting the long-standing rule of mode decoupling. However, these studies have ignored the non-linearities in the isolators. In this work, we consider stiffness nonlinearity from pneumatic isolators and study the nonlinear free undamped vibrations of a passively-isolated ultra-precision manufacturing (UPM) machine. Experimental analysis is conducted to guide the mathematical formulation. The system comprises linearly and nonlinearly coupled in-plane horizontal and rotational motion of the UPM machine with quadratic nonlinear stiffness from the isolators. We present closed-form expressions using the method of multiple scales for two cases viz. the non-resonant case and the bounded internal resonance case. We validate our theoretical findings through direct numerical simulations. For the non-resonant case, we show that the system behaves similar to a linear system. However, for the nearly internal resonance case, we demonstrate strong energy exchange between the modes stemming from nonlinear mode coupling. We further study the effect of nonlinear mode coupling on the vibration isolation performance and demonstrate that mode coupling is not always desirable.
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- Award ID(s):
- 2000984
- PAR ID:
- 10229180
- Date Published:
- Journal Name:
- Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The inerter pendulum vibration absorber is connected with a power take-off mechanism (called IPVA-PTO) to study its wave energy conversion potential. The resulting IPVA-PTO system is integrated between a spar and a floater (torus) using a ballscrew mechanism. The hydrodynamic stiffness, added mass and radiation damping effects on the spar-floater system are characterized using boundary element method via Ansys Aqwa. It has been observed that a 1:2 internal resonance between the spar-floater system and the pendulum is responsible for nonlinear energy transfer between the two systems. This nonlinear energy transfer occurs when the primary harmonic solution of the system becomes unstable, and a secondary solution emerges in the system characterized by harmonics of frequency half the excitation frequency. As a result of this energy transfer, the vibration of the spar-floater system is suppressed, and the energy is transferred to the pendulum. The focus of this paper is to analyze this 1:2 internal resonance phenomenon near the resonant frequency of the spar. The IPVA-PTO system, when integrated with the spar-floater system, is compared to a linear coupling between the spar and the floater in terms of the response amplitude operator (RAO) of the spar and the energy conversion capability defined by the capture width of the energy converter.more » « less
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null (Ed.)Floor isolation systems (FISs) are used to mitigate earthquake-induced damage to sensitive building contents and equipment. Traditionally, the isolated floor and the primary building structure (PS) are analyzed independently, assuming the PS response is uncoupled from the FIS response. Dynamic coupling may be non-negligible when nonlinearities are present under large deflections at strong disturbance levels. This study investigates a multi-functional FIS that functions primarily as an isolator (i.e., attenuating total acceleration sustained by the isolated equipment) at low-to-moderate disturbance levels, and then passively adapt under strong disturbances to function as a nonlinear (vibro-impact) dynamic vibration absorbers to protect the PS (i.e., reducing inter-story drifts). The FIS, therefore, functions as a dual-model vibration isolator/absorber system, with displacement dependent response adaptation. A scale experimental model—consisting of a three-story frame and an isolated mass—is used to demonstrate and evaluate the design methodology via shake table tests. The properties of the 3D-printed rolling pendulum (RP) bearing, the seismic gap, and the impact mechanism are optimized to achieve the desired dual-mode performance. A suite of four ground motions with varying spectral qualities are used, and their amplitudes are scaled to represent various hazards—from service level earthquake (SLE), to design basis earthquake (DBE), and even maximum considered earthquake (MCE). The performance of the multi-functional FIS is established and is described in this paper.more » « less
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Abstract Floor isolation systems (FISs) are used to mitigate earthquake‐induced damage to sensitive building contents. Dynamic coupling between the FIS and primary structure (PS) may be nonnegligible or even advantageous when strong nonlinearities are present under large isolator displacements. This study investigates the influence of dynamic coupling between the PS and FIS in the presence of nonsmooth (impact‐like) nonlinearity in the FIS under intense earthquakes. Using component mode analysis, a nonlinear reduced order model of the combined FIS–PS system is developed by coupling a condensed model of the linear PS to the nonlinear FIS. A bilinear Hertz‐type contact model is assumed for the FIS, with the gap and the impact stiffness and damping providing parametric variation. The performance of the FIS–PS system is quantified through a multiobjective, risk‐based design criterion considering both the total acceleration sustained by the isolated mass under a service‐level earthquake and the interstory drift under a maximum considered earthquake. The results of a parametric study shed light on understanding the valid range that the decoupled approach can be reliably applied for nonlinear FISs experiencing impacts. It is also shown that the nonlinear FIS can be tuned in such a way to mitigate seismic responses of the supporting PS under strong shaking, in addition to protecting the isolated mass at low to moderate shaking. The FIS, therefore, functions as a dual‐mode vibration isolator/absorber system, with displacement‐dependent response adaptation. Guidelines to the optimal tuning of such a dual‐mode system are presented based on the risk‐based stochastic design optimization.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1115/DETC2020-22398
