Two-to-one internal resonance in the higher-order modes of a MEMS beam: Experimental investigation and theoretical analysis via local stability theory

Ruzziconi, Laura; Jaber, Nizar; Kosuru, Lakshmoji; Bellaredj, Mohammed Lamine Faycal; Younis, Mohammad I.

doi:10.1016/j.ijnonlinmec.2020.103664

Cited by 22 publications

(9 citation statements)

References 52 publications

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“…Kirkendall and Kwon [6] detect nested regions of multistability at internal resonance in an electrostatic crystal plate, where the ensuing nonlinear modal interaction can generate topologically distinct dynamics over the parameter space, and the increased complexity related to the internal resonance activation provides a considerable versatility of the device response. Ruzziconi et al [7] analyze a 2:1 internal resonance experimentally arising in the higher-order modes of a MEMS microbeam, and examine the changes induced in the dynamical response, including a phase shift that can be experienced among the modes, alerting that the internal resonance may affect the occurrence of the ultimate dynamic pull-in threshold.…”

Section: Introductionmentioning

confidence: 99%

Combined internal resonances at crossover of slacked micromachined resonators

et al. 2022

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The dynamics of micro-/nanoelectromechanical systems (M/NEMS) curved beams have been thoroughly investigated in the literature, commonly for curved arch beams actuated with electrodes facing their concave surface. Except for few works on slacked carbon nanotubes, the literature lacks a deep understanding of the dynamics of slacked curved resonators, where the electrode is placed in front of the convex beam surface. This paper investigates the dynamics of slacked curved resonators as experiencing combined internal resonances. The curved slacked resonator is excited using an antisymmetric partial electrode while the electrostatic voltage load is driven to elevated excitations, which breaks the symmetry of the system and affects natural frequencies and corresponding mode shapes. The axial load is tuned to monitor the ratios between the natural frequencies of different vibration modes, which induces simultaneous 1:1 and 2:1 internal resonances between the first and second mode with the third. We observe the interaction of hardening and softening bending of the fundamental backbone curves triggering various patterns of the response scenario and the appearance of coexisting regions of irregular dynamics.

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Section: Introductionmentioning

confidence: 99%

Combined internal resonances at crossover of slacked micromachined resonators

et al. 2022

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“…We focus on the 2:1 internal resonance arising in a microbeam-based MEMS device at the third mode dynamics. The main features were previously examined both experimentally and theoretically in Ruzziconi et al [25], to which we refer for more details. The present section briefly recalls the main aspects and further completes the analysis.…”

Section: The 2:1 Internal Resonancementioning

confidence: 99%

“…The present paper is focused on the 2:1 internal resonance arising in a microbeam-based MEMS device. This device was previously analyzed in Ruzziconi et al [25], where an in-depth experimental and theoretical investigation of the dynamics induced by the 2:1 internal resonance was performed. Starting from these results, the present paper further deepens the analysis, by investigating the nonlinear interaction extensively.…”

Section: Introductionmentioning

confidence: 99%

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

et al. 2021

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This work investigates the dynamics of a microbeam-based MEMS device in the neighborhood of a 2:1 internal resonance between the third and fifth vibration modes. The saturation of the third mode and the concurrent activation of the fifth are observed. The main features are analyzed extensively, both experimentally and theoretically. We experimentally observe that the complexity induced by the 2:1 internal resonance covers a wide driving frequency range. Constantly comparing with the experimental data, the response is examined from a global perspective, by analyzing the attractor-basins scenario. This analysis is conducted both in the thirdmode and fifth-mode planes. We show several metamorphoses occurring as proceeding from the principal resonance to the 2:1 internal resonance, up to the final disappearance of the resonant and non-resonant attractors. The shape and wideness of all the basins are examined. Despite they are progressively eroded, an appreciable region is detected where the compact cores of the attractors involved in the 2:1 internal resonance remain substantial, which allows effectively operating them under realistic conditions. The dynamical integrity of each resonant branch is discussed, especially as approaching the bifurcation points where the system becomes more vulnerable to the dynamic pull-in instability.

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“…Besides, the corresponding equipment aiming at measuring resonant frequency shift has proven to reach a high resolution, which further enhances the MEMS sensors' sensitivity [14,15]. In addition, the structure's nonlinearity features appear in the frequency response [16,17], especially jump or bifurcation, further enhancing the detection process [18].…”

Section: Introductionmentioning

confidence: 99%

A multi-sensing scheme based on nonlinear coupled micromachined resonators

et al. 2023

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A new multi-sensing scheme via nonlinear weakly coupled resonators is introduced in this paper, which can simultaneously detect two different physical stimuli by monitoring the dynamic response around the first two lowest modes. The system consists of a mechanically coupled bridge resonator and cantilever resonator. The eigenvalue problem is solved to identify the right geometry for the resonators to optimize their resonance frequencies based on mode localization in order to provide outstanding sensitivity. A nonlinear equivalent model is developed using the Euler–Bernoulli beam theory while accounting for the geometric and electrostatic nonlinearities. The sensor's dynamics are explored using a reduced-order model based on two-mode Galerkin discretization, which reveals the richness of the response. To demonstrate the proposed sensing scheme, the dynamic response of the weakly coupled resonator is investigated by tuning the stiffness and mass of the bridge and cantilever resonators, respectively. With its simple and scalable design, the proposed system shows great potential for intelligent multi-sensing detection in many applications.

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Two-to-one internal resonance in the higher-order modes of a MEMS beam: Experimental investigation and theoretical analysis via local stability theory

Cited by 22 publications

References 52 publications

Combined internal resonances at crossover of slacked micromachined resonators

Combined internal resonances at crossover of slacked micromachined resonators

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

A multi-sensing scheme based on nonlinear coupled micromachined resonators

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