Vibrations of post-buckled rods: The singular inextensible limit

Neukirch, Sébastien; Frelat, Joël; Goriely, Alain; Maurini, Corrado

doi:10.1016/j.jsv.2011.09.021

Cited by 44 publications

(43 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To determine eigenfunctions, we are only interested in non-trivial solutions. These exist if and only if the corresponding determinant vanishes, which can be re-arranged to [47] τ 0 2Ω = cosh α + cos α − − 1 sinh α + sin α − .…”

Section: Appendix C Linear Stability At Zero Voltagementioning

confidence: 99%

Pull-in dynamics of overdamped microbeams

Gomez

Vella

Moulton

2018

J. Micromech. Microeng.

View full text Add to dashboard Cite

We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At DC voltages close to the pull-in voltage, experiments and numerical simulations have reported 'bottleneck' behaviour in which the transient dynamics slow down considerably. This slowing down is highly sensitive to external forces, and so has widespread potential for applications that use pull-in time as a sensing mechanism, including high-resolution accelerometers and pressure sensors. Previously, the bottleneck phenomenon has only been understood using lumped mass-spring models that do not account for effects such as variable residual stress and different boundary conditions. We extend these studies to incorporate the beam geometry, developing an asymptotic method to analyse the pull-in dynamics. We attribute bottleneck behaviour to critical slowing down near the pull-in transition, and we obtain a simple expression for the pull-in time in terms of the beam parameters and external damping coefficient. This expression is found to agree well with previous experiments and numerical simulations that incorporate more realistic models of squeeze film damping, and so provides a useful design rule for sensing applications. We also consider the accuracy of a single-mode approximation of the microbeam equations -an approach that is commonly used to make analytical progress, without systematic investigation of its accuracy. By comparing to our bottleneck analysis, we identify the factors that control the error of this approach, and we demonstrate that this error can indeed be very small.

show abstract

Section: Appendix C Linear Stability At Zero Voltagementioning

confidence: 99%

Pull-in dynamics of overdamped microbeams

Gomez

Vella

Moulton

2018

J. Micromech. Microeng.

View full text Add to dashboard Cite

show abstract

“…While this is true for objects with arbitrarily small thickness, any real object has a finite, if small thickness, and so is, to a certain extent, extensible. The effect of finite extensibility on the buckling of the classical Elastica has been studied by a number of authors [17,18,19]. These analyses reveal that the crucial parameter governing the importance of extensibility is the ratio of the thickness, t, and total length, L tot , of the beam or, equivalently, the von Kármán number, γ = t 2 /(12L 2 tot ).…”

Section: Introductionmentioning

confidence: 99%

The role of extensibility in the birth of a ruck in a rug

Lee

Gouellec

Vella

2015

Extreme Mechanics Letters

View full text Add to dashboard Cite

Everyday experience suggests that a 'ruck' forms when the two ends of a heavy carpet or rug are brought closer together. Classical analysis, however, shows that the horizontal compressive force needed to create such a ruck should be infinite. We show that this apparent paradox is due to the assumption of inextensibility of the rug. By accounting for a finite extensibility, we show that rucks appear with a finite, non-zero end-shortening and confirm our theoretical results with simple experiments. Finally, we note that the appropriate measure of extensibility, the stretchability, is in this case not determined purely by geometry, but incorporates the mechanics of the sheet.

show abstract

“…Note that even though the undulated beam model [16] is relatively easy to use, it is only applicable when the beam is slightly undulated, otherwise significant error will be induced. Since serpentine interconnects usually exhibit severely undulated geometry incorporated by the presence of the additional winding parameter, the elastica model must be used to determine its deformation [20,15] and its dynamic behaviour [21].…”

Section: Numerical Studymentioning

confidence: 99%

Band Gap Formation and Tunability in Stretchable Serpentine Interconnects

Zhang

Parnell

2017

Journal of Applied Mechanics

View full text Add to dashboard Cite

Serpentine interconnects are highly stretchable and frequently used in flexible electronic systems. In this work, we show that the undulating geometry of the serpentine interconnects will generate phononic band gaps to manipulate elastic wave propagation. The interesting effect of 'bands-sticking-together' is observed. We further illustrate that the band structures of the serpentine interconnects can be tuned by applying pre-stretch deformation. The discovery offers a way to design stretchable and tunable phononic crystals by using metallic interconnects instead of the conventional design with soft rubbers and unfavorable damping.

show abstract

Vibrations of post-buckled rods: The singular inextensible limit

Cited by 44 publications

References 16 publications

Pull-in dynamics of overdamped microbeams

Pull-in dynamics of overdamped microbeams

The role of extensibility in the birth of a ruck in a rug

Band Gap Formation and Tunability in Stretchable Serpentine Interconnects

Contact Info

Product

Resources

About