Experimental and theoretical investigation of the 2:1 internal resonance in the higher-order modes of a MEMS microbeam at elevated excitations

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

doi:10.1016/j.jsv.2021.115983

Cited by 15 publications

(4 citation statements)

References 40 publications

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“…For example, Kes ¸kekler et al [35] demonstrated the ZD point with 2:1 InRes in a graphene nano-mechanical resonator due to graphene's strong hardening effect and interpreted this as tailoring non-linear damping using 2:1 InRes. Ruzziconi et al [36] analyzed the 2:1 InRes dynamics of a microbeam resonator with cubic coupling and hardening nonlinearity in the presence of quadratic nonlinearity from electrostatic actuation. Although these studies on 2:1 InRes explored the Duffing hardening effect, a comprehensive analysis of the ZD effect in a 1:2 or 2:1 InRes systems for frequency stabilization has not been conducted.…”

Section: Introductionmentioning

confidence: 99%

One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity

Yu,

Donmez,

Herath

et al. 2023

J. Micromech. Microeng.

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This paper investigates the implementation of 1:2 internal resonance (InRes) in a clamped-clamped stepped beam resonator with a strong Duffing effect, focusing on its potential for frequency stabilization in MEMS resonators. InRes can arise in a nonlinear system of which mode frequencies are close to an integer ratio, facilitating the internal exchange of energy from an externally driven mode to an undriven mode. The presence of 1:2 InRes and Duffing hardening nonlinearity can result in frequency saturation phenomena, leading to a flat amplitude-frequency response range, which forms the basis for frequency stabilization. The stepped beam resonator design, combined with thermal frequency tuning, enables precise alteration of the frequency ratio between the second and third flexural modes required to achieve the desired 1:2 ratio for InRes. Experimental characterization and theoretical analysis revealed that frequency mismatch plays a significant role, with larger mismatch conditions leading to stronger energy exchange and a wider range of drive force for frequency saturation. The study highlights the frequency saturation mechanism utilizing 1:2 InRes and emphasizes the advantage of Duffing nonlinearity and larger intermodal frequency mismatch for broader frequency stabilization, providing valuable insights for the design and optimization of MEMS resonators.

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Section: Introductionmentioning

confidence: 99%

One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity

Yu,

Donmez,

Herath

et al. 2023

J. Micromech. Microeng.

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“…A sudden collapse into the fixed electrode, also known as the pull-in instability, occurs if the voltage exceeds a critical value. The static and dynamic behaviours were investigated in depth in the literature theoretically and experimentally due to the continuously increasing exploitation of these microsystems [19,[24][25][26][27][28]. Analysing the behaviour of these resonators is commonly based on the classical model (Euler-Bernoulli beam theory) or the nonclassical mechanical model of the beam.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear damping in micromachined bridge resonators

et al. 2022

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This study presents a thorough theoretical and experimental investigation on the nonlinear damping of in-plane micromachined electromechanical resonators. More specifically, experiments are conducted on an electrically actuated bridge resonator, and the primary resonance response of the system is obtained at various AC and DC voltages. A nonlinear theoretical model is developed using the Euler–Bernoulli beam theory while accounting for the geometric, electrostatic (including fringing field effect), and damping nonlinearities. Two damping models are considered in the theoretical model: the Kelvin–Voigt model, which for this system is a nonlinear damping model due to the presence of geometric nonlinearities. The second damping model consists of linear, quadratic, and cubic damping terms. A high-dimensional discretisation is performed, and the nonlinear dynamics of the resonator are examined in detail in the primary resonance regime by constructing the frequency response diagrams at various AC and DC voltages. Thorough comparisons are conducted between the experimental data and the theoretical results for different damping conditions. It is shown that the microresonator displays strong nonlinear damping. Detailed calibration procedures for the nonlinear damping models are proposed, and the advantages and disadvantages of each nonlinear damping model are discussed.

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“…They concluded that an increased excitation amplitude widens the frequency bandwidth. More recently, Ruzziconi et al [21] experimentally and numerically analyzed the internal resonance in a MEMS CL-CL microbeam including higher-order vibration modes and found more complex dynamic behavior such as the coexistence of different attractors and a phase shift through the resonant branch.…”

Section: Introductionmentioning

confidence: 99%

Internal resonance in a MEMS levitation force resonator

Zamanzadeh

Meijer²,

Ouakad³

2022

Nonlinear Dyn

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In this work, we explore internal resonances in a levitation force microelectromechanical system-based actuator assuming flexible cantilever and clamped-clamped microbeam configurations. The levitation force is generated through a special arrangement of two-side stationary charged substrates and a central grounded stationary strip. The design assumes as well an upper flexible microbeam strip. The DC part of the excitation voltage pushes up the moving microbeam away from its lower stationary electrode. A superimposed harmonic AC voltage lets the flexible strip vibrate around its equilibrium position. Energy exchange among the computed lower vibration frequencies and their respective frequency and force response curves are explored for possibilities of principal parametric and internal resonances interactions. The generated responses are computed using the bifurcation toolbox MatCont. The effect of Von Karman nonlinearity to power the energy exchange within vibration modes is explored and dominant factors in

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Experimental and theoretical investigation of the 2:1 internal resonance in the higher-order modes of a MEMS microbeam at elevated excitations

Cited by 15 publications

References 40 publications

One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity

One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity

Nonlinear damping in micromachined bridge resonators

Internal resonance in a MEMS levitation force resonator

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