Modal interactions of flexural and torsional vibrations in a microcantilever

Westra, H.J.R.; Zant, Herre S. J. van der; Venstra, Warner J.

doi:10.1016/j.ultramic.2012.06.010

Cited by 21 publications

(13 citation statements)

References 24 publications

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“…In addition, the modal interaction strength can continuously by tuned from

(stiffening) to

(softening), which is about 6 orders of magnitude larger than that in micromechanical resonators [ 46 ]. The nonlinear intrinsic coupling between the flexural–flexural, torsional–torsional and flexural–torsional modes of a microcantilever was experimentally reported in [ 351 ]. The direct bending-induced nonlinearities can be identified to facilitate the precise tuning of nanomechanical resonators [ 352 ].…”

Section: Active Frequency Tuning Methodsmentioning

confidence: 99%

Tunable Micro- and Nanomechanical Resonators

Zhang

Peng

et al. 2015

Sensors

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Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.

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“…In addition, the modal interaction strength can continuously by tuned from

(stiffening) to

Section: Active Frequency Tuning Methodsmentioning

confidence: 99%

Tunable Micro- and Nanomechanical Resonators

Zhang

Peng

et al. 2015

Sensors

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show abstract

“…This results in a strong coupling between the transverse (bending) and axial (stretching) motions of the main beam, leading to nonlinear geometric effects [38]. Such nonlinearity is reminiscent of a number of applications in aeronautics and micro-mechanics where nonlinearity arises from finite displacements [39][40][41]. Two masses of 0.218 kg each are attached to the cross-beam with set screws in order to provide a means of adjusting both the torsional inertia and the symmetry of the system.…”

Section: Example Structure-a Beam With Two Closely Spaced Modesmentioning

confidence: 99%

Force appropriation of nonlinear structures

Renson¹,

Hill²,

Ehrhardt

et al. 2018

Proc. R. Soc. A.

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Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the system response and the applied excitation. This paper demonstrates that this commonly used quadrature condition can give results that are significantly different from the true NNM, in particular, when the excitation applied to the system is limited to one input force, as is frequently used in practice. The system studied is a clamped–clamped cross-beam with two closely spaced modes. This paper shows that the regions where the quadrature condition is (in)accurate can be qualitatively captured by analysing transfer of energy between the modes of the system, leading to a discussion of the appropriate number of input forces and their locations across the structure.

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“…This phenomenon can be the consequence of the coupling between the system vibrational modes, therefore generating an internal resonance and energy exchange between the modes [29]. Such nonlinear interactions have been studied in numerous systems ranging from macro, micro, and nano-scale [30][31][32][33][34]. These micro/nano structures have been shown to exhibit two-to-one [30][31][32], three-to-one [33], and one-to-one [34] internal resonances.…”

Section: Introductionmentioning

confidence: 99%

One-to-One and Three-to-One Internal Resonances in MEMS Shallow Arches

Ouakad

Sedighi

Younis

2017

Journal of Computational and Nonlinear Dynamics

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The nonlinear modal coupling between the vibration modes of an arch-shaped microstructure is an interesting phenomenon, which may have desirable features for numerous applications, such as vibration-based energy harvesters. This work presents an investigation into the potential nonlinear internal resonances of a microelectromechanical systems (MEMS) arch when excited by static (DC) and dynamic (AC) electric forces. The influences of initial rise and midplane stretching are considered. The cases of one-to-one and three-to-one internal resonances are studied using the method of multiple scales and the direct attack of the partial differential equation of motion. It is shown that for certain initial rises, it is possible to activate a three-to-one internal resonance between the first and third symmetric modes. Also, using an antisymmetric half-electrode actuation, a one-to-one internal resonance between the first symmetric and the second antisymmetric modes is demonstrated. These results can shed light on such interactions that are commonly found on micro and nanostructures, such as carbon nanotubes.

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Modal interactions of flexural and torsional vibrations in a microcantilever

Cited by 21 publications

References 24 publications

Tunable Micro- and Nanomechanical Resonators

Tunable Micro- and Nanomechanical Resonators

Force appropriation of nonlinear structures

One-to-One and Three-to-One Internal Resonances in MEMS Shallow Arches

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