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.
In this paper, we report the first experimental observation of internal resonance in a dusty plasma, which shows the intrinsic nonlinearities of dust interactions in plasmas. When driving a system of vertically aligned dust particle pairs in the vertical direction, the horizontal motion is found to be excited during onset of internal resonance when the higher-frequency horizontal sloshing mode is nonlinearly coupled to the vertical breathing mode through the 1:2 commensurable relation. A theoretical model of the nonlinear interaction of dust particles in plasma is also provided and the results of the theoretical model are shown to match experimental observations.
- Award ID(s):
- 1740203
- Publication Date:
- NSF-PAR ID:
- 10303219
- Journal Name:
- New Journal of Physics
- Volume:
- 21
- Issue:
- 10
- Page Range or eLocation-ID:
- Article No. 103051
- ISSN:
- 1367-2630
- Publisher:
- IOP Publishing
- Sponsoring Org:
- National Science Foundation
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