iMechanica - snap-through instability
https://imechanica.org/taxonomy/term/3533
enDelayed bifurcation in elastic snap-through instabilities
https://imechanica.org/node/25146
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/3369">bifurcation</a></div><div class="field-item odd"><a href="/taxonomy/term/3533">snap-through instability</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Liu, M., Gomez, M., & Vella, D.* (2021). <a href="https://doi.org/10.1016/j.jmps.2021.104386">Delayed bifurcation in elastic snap-through instabilities.</a> <em>J Mech. Phys. Solids</em>, 151, 104386.</p>
<p><img src="https://ars.els-cdn.com/content/image/1-s2.0-S0022509621000727-gr1_lrg.jpg" width="382" height="142" /> <img src="https://ars.els-cdn.com/content/image/1-s2.0-S0022509621000727-gr7_lrg.jpg" width="205" height="141" /></p>
<p>We study elastic snap-through induced by a control parameter that evolves dynamically. In particular, we study an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening the arch is bistable but, below a critical end-shortening, the arch becomes monostable. We study when and how the arch transitions between states and show that the end-shortening at which the fast ‘snap’ happens depends on the rate at which the end-shortening is reduced. This delay in snap-through is a consequence of delayed bifurcation and occurs even in the perfectly elastic case when viscous (and viscoelastic) effects are negligible. We present the results of numerical simulations to determine the magnitude of this delay (and the associated time lag) as the loading rate and the importance of external viscous damping vary. We also present an asymptotic analysis of the geometrically-nonlinear problem that reduces the salient dynamics to that of an ordinary differential equation; the form of this reduced equation is generic for snap-through instabilities in which the relevant control parameter is ramped linearly in time. Moreover, this asymptotic reduction allows us to derive analytical results for the delay observed in snap-through that are in good agreement with the results of our simulations. Finally, we discuss scaling laws for the delay that should be expected in other examples of delayed bifurcation in elastic instabilities.</p>
<p><a href="https://www.researchgate.net/publication/349747992_Delayed_bifurcation_in_elastic_snap-through_instabilities">https://www.researchgate.net/publication/349747992_Delayed_bifurcation_i...</a></p>
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<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://imechanica.org/files/JMPS-2021-Delayed%20bifurcation%20in%20elastic%20snap-through%20instabilities.pdf" type="application/pdf; length=1998680" title="JMPS-2021-Delayed bifurcation in elastic snap-through instabilities.pdf">JMPS-2021-Delayed bifurcation in elastic snap-through instabilities</a></span></td><td>1.91 MB</td> </tr>
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</div></div></div>Mon, 03 May 2021 09:48:25 +0000Mingchao Liu25146 at https://imechanica.orghttps://imechanica.org/node/25146#commentshttps://imechanica.org/crss/node/25146Bistable Auxetic Mechanical Metamaterials
https://imechanica.org/node/20394
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10624">auxetic</a></div><div class="field-item odd"><a href="/taxonomy/term/9428">mechanical metamaterials</a></div><div class="field-item even"><a href="/taxonomy/term/2068">bistable structure</a></div><div class="field-item odd"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item even"><a href="/taxonomy/term/10994">Negative Poisson's ratio</a></div><div class="field-item odd"><a href="/taxonomy/term/10613">architected materials</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p> </p>
<p><img src="http://scholar.harvard.edu/files/rafsanjani/files/bistable_auxetic.jpg" alt="" width="600" height="300" /></p>
<p><span>A. Rafsanjani and D. Pasini, </span><strong>Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs</strong><span>. </span><a href="http://dx.doi.org/10.1016/j.eml.2016.09.001" target="_blank">Extreme Mechanics Letters</a><span> 9, 291-296 (2016).</span></p>
<p>ABSTRACT Auxetic materials become thicker rather than thinner when stretched, exhibiting an unusual negative Poisson’s ratio well suited for designing shape transforming metamaterials. Current auxetic designs, however, are often monostable and cannot maintain the transformed shape upon load removal. Here, inspired by ancient geometric motifs arranged in square and triangular grids, we introduce a class of switchable architected materials exhibiting simultaneous auxeticity and structural bistability. The material concept is experimentally realized by perforating various cut motifs into a sheet of rubber, thus creating a network of rotating units connected with compliant hinges. The metamaterial performance is assessed through mechanical testing and accurately predicted by a coherent set of finite element simulations. A discussion on a rich set of mechanical phenomena follows to shed light on the main design principles governing bistable auxetics.</p>
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<p><iframe src="https://player.vimeo.com/video/196185494" frameborder="0" width="640" height="360"></iframe></p>
<p><a href="https://vimeo.com/196185494"> </a></p>
</div></div></div>Mon, 03 Oct 2016 03:03:43 +0000Ahmad Rafsanjani20394 at https://imechanica.orghttps://imechanica.org/node/20394#commentshttps://imechanica.org/crss/node/20394Snapping Mechanical Metamaterials under Tension
https://imechanica.org/node/18994
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/9428">mechanical metamaterials</a></div><div class="field-item odd"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item even"><a href="/taxonomy/term/10613">architected materials</a></div><div class="field-item odd"><a href="/taxonomy/term/1882">advanced materials</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><img src="http://pasini.ca/wp-content/uploads/2015/09/snapping_metamaterial.png" alt="snapping metamaterials" width="640" height="240" /></p>
<p>We present a monolithic mechanical metamaterial comprising a periodic arrangement of snapping units with tunable tensile behavior. Under tension, the metamaterial undergoes a large extension caused by sequential snap-through instabilities, and exhibits a pattern switch from an undeformed wavy-shape to a diamond configuration. By means of experiments performed on 3D printed prototypes, numerical simulations, and theoretical modeling, we demonstrate how the snapping architecture can be tuned to generate a range of nonlinear mechanical responses including monotonic, S-shaped, plateau, and non-monotonic snap-through behavior. This work contributes to the development of micro-architectured materials with programmable nonlinear mechanical responses. </p>
<p>Rafsanjani A, Akbarzadeh AH, Pasini D, Snapping Mechanical Metamaterials under Tension, <a class="links" title="link to article" href="http://dx.doi.org/10.1002/adma.201502809" target="_blank">Advanced Materials</a> 27: 5931-5935 (2015).</p>
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<iframe src="https://player.vimeo.com/video/143506750" frameborder="0" width="500" height="281"></iframe>
</div></div></div>Thu, 15 Oct 2015 16:11:31 +0000Ahmad Rafsanjani18994 at https://imechanica.orghttps://imechanica.org/node/18994#commentshttps://imechanica.org/crss/node/18994Amplifying the response of soft actuators by harnessing snap-through instabilities
https://imechanica.org/node/18758
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10718">soft actuator</a></div><div class="field-item odd"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item even"><a href="/taxonomy/term/10719">fluidic segment</a></div><div class="field-item odd"><a href="/taxonomy/term/10720">amplification</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Engineering actuators with capabilities that match and even exceed those found in nature, is a long-standing challenge. While traditional actuators are built with hard materials, it has been recently shown that elastomeric materials enable the design of fluidic actuators that are lightweight, inexpensive, easy to fabricate, and able to undergo large deformation and complex motions. However, these actuators typically rely on large volumes for their actuation. This requirement limits the performance of soft actuators, since it makes the rate of actuation slow and it requires the system to be in the vicinity of a large reservoir. There is a need for new designs of soft actuators that reduce the amount of fluid needed for actuation, and thus increase their actuation speed and allow for more compact systems.</p>
<p>While instabilities have traditionally been avoided as they often represent mechanical failure, in this work we embrace them to amplify the response of fluidic soft actuators. Besides presenting a robust strategy to trigger snap-through instabilities at constant volume in soft fluidic actuators, we also show that the energy released at the onset of the instabilities can be harnessed to trigger instantaneous and significant changes in internal pressure, extension, shape and exerted force. Therefore, in stark contrast to previously studied soft fluidic actuators, we demonstrate that by harnessing snap-through instabilities it is possible to design and construct systems with highly controllable non-linear behavior, in which small amounts of fluid suffice to instantaneously trigger large outputs.</p>
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<p><a href="https://www.youtube.com/watch?v=ryY1A-Cz5-A">Link to video</a></p>
<p><a href="http://www.seas.harvard.edu/news/2015/08/controlling-uncontrollable">Linkt to news article</a></p>
<p><a href="http://www.pnas.org/content/early/2015/08/13/1504947112.abstract">Overvelde, J. T. B., Kloek, T., D’haen, J. J. A., Bertoldi, K., (2015) Amplifying the Response of Soft Actuators by Harnessing Snap-through Instabilities. <em>Proceedings of the National Academy of Sciences of the United States of America.</em></a></p>
</div></div></div>Tue, 25 Aug 2015 14:50:58 +0000Johannes T.B. Overvelde18758 at https://imechanica.orghttps://imechanica.org/node/18758#commentshttps://imechanica.org/crss/node/18758Harnessing snap-through instability in soft dielectrics to achieve giant voltage-triggered deformation
https://imechanica.org/node/11345
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/85">suo group research</a></div><div class="field-item odd"><a href="/taxonomy/term/472">large deformation</a></div><div class="field-item even"><a href="/taxonomy/term/992">dielectric elastomer</a></div><div class="field-item odd"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item even"><a href="/taxonomy/term/6392">soft dielectrics</a></div><div class="field-item odd"><a href="/taxonomy/term/6673">bauer group research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
<span>For a dielectric elastomer membrane we show giant voltage-triggered expansion of area by 1692%, far beyond the largest values reported in the literature.</span>
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A soft dielectric membrane is prone to snap-through instability. We present theory and experiment to show that the instability can be harnessed to achieve giant voltage-triggered deformation.We mount a membrane on a chamber of a suitable volume, pressurize the membrane into a state near the verge of the instability, and apply a voltage to trigger the snap without causing electrical breakdown. For an acrylic membrane we demonstrate voltage-triggered expansion of area by 1692%, far beyond the largest value reported in the literature. The large expansion can even be retained after the voltage is switched off.
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<em>The paper is now published on the web:</em>
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<p><em><strong>Soft Matter</strong></em>, 2012, <strong>8</strong>, 285-288</p>
<p><span class="DOILink"><strong>DOI:</strong> 10.1039/C1SM06736B</span> </p>
<p><a href="http://xlink.rsc.org/?doi=C1SM06736B">http://xlink.rsc.org/?doi=C1SM06736B</a></p>
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<em>The visualization below appears on the front cover of Soft Matter:</em>
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<img src="files/images/cover%20image.preview.png" alt=" " width="369" height="301" /></p>
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<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/x-pdf" src="/modules/file/icons/application-octet-stream.png" /> <a href="https://imechanica.org/files/Keplinger%20et%20al_Harnessing%20snap%20through_Soft%20Matter_2012.pdf" type="application/x-pdf; length=1097976" title="Keplinger et al_Harnessing snap through_Soft Matter_2012.pdf">Keplinger et al_Harnessing snap through_Soft Matter_2012.pdf</a></span></td><td>1.05 MB</td> </tr>
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</div></div></div>Fri, 28 Oct 2011 17:54:35 +0000Christoph Keplinger11345 at https://imechanica.orghttps://imechanica.org/node/11345#commentshttps://imechanica.org/crss/node/11345Harnessing snap-through instability in soft dielectrics to achieve giant voltage-triggered deformation
https://imechanica.org/node/11344
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-taxonomyextra field-type-taxonomy-term-reference field-label-above"><div class="field-label">Taxonomy upgrade extras: </div><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div><div class="field-item odd"><a href="/taxonomy/term/85">suo group research</a></div><div class="field-item even"><a href="/taxonomy/term/472">large deformation</a></div><div class="field-item odd"><a href="/taxonomy/term/992">dielectric elastomer</a></div><div class="field-item even"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item odd"><a href="/taxonomy/term/6392">soft dielectrics</a></div><div class="field-item even"><a href="/taxonomy/term/6673">bauer group research</a></div></div></div>Fri, 28 Oct 2011 17:19:09 +0000Christoph Keplinger11344 at https://imechanica.orghttps://imechanica.org/node/11344#commentshttps://imechanica.org/crss/node/11344Harnessing snap-through instability in soft dielectrics to achieve giant voltage-triggered deformation
https://imechanica.org/node/11343
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>For a dielectric elastomer membrane we show giant voltage-triggered expansion of area by 1692%, far beyond the largest values reported in the literature.</span></p>
</div></div></div><div class="field field-name-taxonomyextra field-type-taxonomy-term-reference field-label-above"><div class="field-label">Taxonomy upgrade extras: </div><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div><div class="field-item odd"><a href="/taxonomy/term/85">suo group research</a></div><div class="field-item even"><a href="/taxonomy/term/472">large deformation</a></div><div class="field-item odd"><a href="/taxonomy/term/992">dielectric elastomer</a></div><div class="field-item even"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item odd"><a href="/taxonomy/term/6392">soft dielectrics</a></div><div class="field-item even"><a href="/taxonomy/term/6673">bauer group research</a></div></div></div>Fri, 28 Oct 2011 16:57:22 +0000Christoph Keplinger11343 at https://imechanica.orghttps://imechanica.org/node/11343#commentshttps://imechanica.org/crss/node/11343Snap-through actuation of thick-wall electroactive balloons
https://imechanica.org/node/10417
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/882">electromechanical instability</a></div><div class="field-item odd"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item even"><a href="/taxonomy/term/5088">large deformations</a></div><div class="field-item odd"><a href="/taxonomy/term/6361">EAP</a></div><div class="field-item even"><a href="/taxonomy/term/6362">microactuators</a></div><div class="field-item odd"><a href="/taxonomy/term/6363">micropumps</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span class="Apple-style-span"><span class="Apple-style-span"><br /><span class="Apple-style-span"></span></span></span></p>
<p><a href="http://dx.doi.org/10.1016/j.ijnonlinmec.2011.05.006">Snap-through actuation of thick-wall electroactive balloons</a> </p>
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<strong>Stephan Rudykh (a),<span class="Apple-converted-space"> (c</span>), Kaushik Bhattacharya </strong><strong>(c) and Gal deBotton (a), (b)</strong>
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(a)<span class="Apple-converted-space"> </span>Department of Mechanical Engineering, Ben-Gurion University, 84105 Beer-Sheva, Israel
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(b)<span class="Apple-converted-space"> </span>Department of Biomedical Engineering, Ben-Gurion University, 84105 Beer-Sheva, Israel
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(c)<span class="Apple-converted-space"> </span>Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, United States
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Abstract</p>
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Solution to the problem of a spherical balloon made out of an electroactive polymer which is subjected to coupled mechanical and electrical excitations is determined. It is found that for certain material behaviors instabilities that correspond to abrupt changes in the balloon size can be triggered. This can be exploited to electrically control different actuation cycles as well as to use the balloon as a micro-pump.
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<a href="http://dx.doi.org/10.1016/j.ijnonlinmec.2011.05.006">DOI:10.1016/j.ijnonlinmec.2011.05.006</a>
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</div></div></div>Wed, 15 Jun 2011 09:36:12 +0000Stephan Rudykh10417 at https://imechanica.orghttps://imechanica.org/node/10417#commentshttps://imechanica.org/crss/node/10417Symmetry breaking, snap-through, and pull-in instabilities under dynamic loading of microelectromechanical shallow arches
https://imechanica.org/node/6597
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/257">MEMS</a></div><div class="field-item odd"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item even"><a href="/taxonomy/term/4277">symmetry breaking</a></div><div class="field-item odd"><a href="/taxonomy/term/4278">pull-in parameters</a></div><div class="field-item even"><a href="/taxonomy/term/4279">bi-stability</a></div><div class="field-item odd"><a href="/taxonomy/term/4280">pseudo-arc-length continuation</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>Arch-shaped microelectromechanical systems (MEMS) have been used as mechanical memories, micro-relays, micro-valves, optical switches, and digital micro-mirrors. A bi-stable structure, such as an arch, is characterized by a multivalued load deflection curve. Here we study the symmetry breaking, the snap-through instability, and the pull-in instability of a bi-stable arch shaped MEMS under static and dynamic electric loads.<!--break--><span> </span><span> </span>Unlike a mechanical load, the electric load is a nonlinear function of the a priori unknown deformed shape of the arch. The nonlinear partial differential equation governing transient deformations of the arch is solved numerically using the Galerkin method and a time integration scheme that adaptively adjusts the time step to compute the solution within the prescribed tolerance. For the static problem, the displacement control and the pseudo-arc length continuation methods are used to obtain the bifurcation curve of arch’s displacement versus a load parameter. The displacement control method fails to compute arch’s asymmetric deformations that are found by the pseudo-arc-length continuation method. For the dynamic problem, two distinct mechanisms of the snap-through instability are found. It is shown that critical loads and geometric parameters for instabilities of an arch under an electric load with and without the consideration of mechanical inertia effects are quite different. A phase diagram between a critical load parameter and the arch height is constructed <span> </span>to delineate different regions of instabilities.<span> </span>We compare results from the present model with those from a continuum mechanics based approach, and with results of other models and experiments available in the literature.<span> </span>The paper is accepted for publication in Smart Materials and Structures. I have attached a preprint.</span></p>
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<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://imechanica.org/files/SMS_Das_Batra_preprint_0.pdf" type="application/pdf; length=898942" title="SMS_Das_Batra_preprint.pdf">SMS_Das_Batra_preprint.pdf</a></span></td><td>877.87 KB</td> </tr>
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</div></div></div>Fri, 07 Aug 2009 14:06:26 +0000kaushik das6597 at https://imechanica.orghttps://imechanica.org/node/6597#commentshttps://imechanica.org/crss/node/6597Pull-in and snap-through instabilities in transient deformations of microelectromechanical systems
https://imechanica.org/node/4924
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/248">finite element analysis</a></div><div class="field-item odd"><a href="/taxonomy/term/257">MEMS</a></div><div class="field-item even"><a href="/taxonomy/term/607">boundary element method</a></div><div class="field-item odd"><a href="/taxonomy/term/3533">snap-through instability</a></div><div class="field-item even"><a href="/taxonomy/term/3534">pull-in instability</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
We analyze transient finite electroelastodynamic deformations of a perfect electrically conducting undamped clamped–clamped beam, a clamped–clamped parabolic arch and a clamped–clamped bell-shaped arch suspended over a flat rigid semi-infinite perfect conductor. The pull-in instability in a beam and the pull-in and the snap-through instabilities in the two arches due to time-dependent potential difference between the two electrodes have been studied. The potential difference is applied either suddenly or is increased linearly in time. Since the time scale of the transient electric forces is very small as compared to that of the mechanical forces, inertia effects only in the mechanical deformations are considered. Effects of both material and geometric nonlinearities are incorporated in the problem formulation and solution; however, damping due to the interaction of the structure with the surrounding medium is neglected. The coupled nonlinear partial differential equations for mechanical deformations are solved numerically by the finite element method and those for the electrical problem by the boundary element method. The Coulomb pressure due to the potential difference between the two electrodes is a nonlinear function of the <em>a priori</em> unknown distance between them. The potential difference that induces either the pull-in instability in a beam or the snap-through followed by the pull-in instabilities in an arch has been computed. Wherever possible these results are compared with those available in the literature. With a decrease in the rate of the applied potential difference, the pull-in and the snap-through parameters approach those for a static problem. Also, for large rates of increase in the potential difference between the two electrodes, the snap-through instability in an arch is suppressed and only the pull-in instability occurs.
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<a href="http://www.iop.org/EJ/abstract/0960-1317/19/3/035008/">http://www.iop.org/EJ/abstract/0960-1317/19/3/035008/</a>
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<a href="http://dx.doi.org/10.1088/0960-1317/19/3/035008">http://dx.doi.org/10.1088/0960-1317/19/3/035008</a>
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</div></div></div>Thu, 26 Feb 2009 21:03:15 +0000kaushik das4924 at https://imechanica.orghttps://imechanica.org/node/4924#commentshttps://imechanica.org/crss/node/4924Error | iMechanica