کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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289641 | 509689 | 2010 | 21 صفحه PDF | دانلود رایگان |
The collective dynamic response of microbeam arrays is governed by nonlinear effects, which have not yet been fully investigated and understood. This work employs a nonlinear continuum-based model in order to investigate the nonlinear dynamic behavior of an array of N nonlinearly coupled micro-electromechanical beams that are parametrically actuated. Investigations focus on the behavior of small size arrays in the one-to-one internal resonance regime, which is generated for low or zero DC voltages. The dynamic equations of motion of a two-element system are solved analytically using the asymptotic multiple-scales method for the weakly nonlinear system. Analytically obtained results are verified numerically and complemented by a numerical analysis of a three-beam array. The dynamic responses of the two- and three-beam systems reveal coexisting periodic and aperiodic solutions. The stability analysis enables construction of a detailed bifurcation structure, which reveals coexisting stable periodic and aperiodic solutions. For zero DC voltage only quasi-periodic and no evidence for the existence of chaotic solutions are observed. This study of small size microbeam arrays yields design criteria, complements the understanding of nonlinear nearest-neighbor interactions, and sheds light on the fundamental understanding of the collective behavior of finite-size arrays.
Journal: Journal of Sound and Vibration - Volume 329, Issue 18, 30 August 2010, Pages 3835–3855