Effects of noise on the internal resonance of a nonlinear oscillator

Zanette, Damián H.

doi:10.1038/s41598-018-24383-2

Cited by 22 publications

(12 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several groups [32,[123][124][125][126][127][128] have developed mathematical models to explain and explore the energy transfer among vibration modes using lumped-mass parameter systems or distributed parameter models using for instance the Euler-Bernoulli beam equation [32,123]. For example, Zanette [125][126][127] performed in-depth theoretical analysis on the modal coupling and energy transfer among vibration modes of micro and nanomechanical systems.…”

Section: Linear and Nonlinear Modal Couplingmentioning

confidence: 99%

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Hajjaj

Jaber

Ilyas

et al. 2020

International Journal of Non-Linear Mechanics

122

View full text Add to dashboard Cite

Micro and nanoelectromechanical systems M/NEMS have been extensively investigated and exploited in the past few decades for various applications and for probing fundamental physical phenomena. Understanding the linear and nonlinear dynamical behaviors of the movable structures in these systems is crucial for their successful implementation in various novel technologies and to meet the long list of new sophisticated requirements. This paper presents a review for some of the recent topics pertaining to the dynamical behaviors, linear and nonlinear, of M/NEMS resonating structures. First, an overview is presented of the various used dynamical approaches to enhance the sensitivity of resonators for sensing applications. Then a summary is presented of the recent works on the linear and nonlinear mode coupling in M/NEMS resonator. Next, recent research is reviewed on coupled M/NEMS resonators, mechanically and electrically, leading to collective behaviors like mode localization. The final part of the paper discusses analytical approaches that have been developed to better understand and investigate the dynamical behavior of M/NEMS resonators focusing on the perturbation method the multiple time scales.

show abstract

Section: Linear and Nonlinear Modal Couplingmentioning

confidence: 99%

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Hajjaj

Jaber

Ilyas

et al. 2020

International Journal of Non-Linear Mechanics

122

View full text Add to dashboard Cite

show abstract

“…Some of the benefits achieved under IR conditions are as follows. •Achieving more robustness to noise at the higher quality factors [ 496 ] and eliminating the electrical noise in the feedback circuit due to sustaining the stable vibrations without external excitation through the energy exchange between coupled modes. [ 444 ] •Enhancing signal gain in high‐quality‐factor vibratory gyroscopes.…”

Section: Fundamental Concepts Of Nano/micromechanical Resonatorsmentioning

confidence: 99%

A Comprehensive Categorization of Micro/Nanomechanical Resonators and Their Practical Applications from an Engineering Perspective: A Review

Ghaemi

Nikoobin

Ashory

2022

Adv Elect Materials

View full text Add to dashboard Cite

Micro/nanoelectromechanical systems (M/NEMS), especially micro/nanomechanical resonators, provide an unprecedented platform for investigating a wide range of applications in both fundamental physical phenomena (such as quantum‐level problems) and engineering and applied sciences (like sensing physical quantities and signal processing). In sensing context, these tiny resonators are invaluable tools for detecting weak forces and single molecules. Measuring such small variations in sub‐nanometer amplitudes at high frequencies has created many practical challenges. Therefore, maximizing the responsivity to a specified input parameter and minimizing the responsivity to other inputs such as noise are considered as the optimal design for the excellent performance in nanoresonators. The present review aims to summarize some of the recent progress in this rapidly advancing field. Specifically, more attention is paid to the topics related to the dynamical behaviors of micro/nanoresonator and their practical applications. First, the theory behind micro/nanoresonators is described. Then a summary is presented of the basic concepts in resonant devices. In addition, several commonly dynamical techniques to enhance sensitivity are introduced. Finally, the devices are classified based on linear and nonlinear, single and array, symmetric and asymmetric, and frequency shift‐based and amplitude shift‐based resonators, along with the relative advantages and disadvantages of each one in engineering applications.

show abstract

“…As a result, there has been significant interest in suppressing the nonlinearity of MEMS resonators to enhance their frequency stability [15][16][17][18][19]. Recently, researchers have proposed utilizing the non-linear phenomenon of internal resonance (InRes) as a new approach to stabilizing frequency fluctuations [20][21][22][23][24][25][26][27][28]. In a non-linear system, InRes can arise in an undriven vibrational mode by internally transferring energy from another vibrational mode that is externally driven when the two modal frequencies are commensurable into an m:n ratio (where m and n are integers) [29,30].…”

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.

View full text Add to dashboard Cite

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.

show abstract

Effects of noise on the internal resonance of a nonlinear oscillator

Cited by 22 publications

References 27 publications

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

A Comprehensive Categorization of Micro/Nanomechanical Resonators and Their Practical Applications from an Engineering Perspective: A Review

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

Contact Info

Product

Resources

About