Elastic instability of nanomechanical beams

Carr, Stephen M; Wybourne, M. N.

doi:10.1063/1.1539924

Cited by 38 publications

(43 citation statements)

References 23 publications

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“…38 Our approach is more general than other approaches used for studying the second-order buckling transition. 39,40 Note that recently there is a growing interest in the buckling of small rods in the context of, e.g., mechanical properties and stability of carbon nanotubes, 41-45 multilayers, 46 biopolymers, 47,48 DNA, 49,50 and fracture. 51,52 A nice modern introduction to the application of buckling to pattern formation in physical and biological systems can be found in Ref.…”

Section: B Novel Order Parameters To Describe Magnetic and Mechanicamentioning

confidence: 98%

Magnetic and mechanical buckling: Modified Landau theory approach to study phase transitions in micromagnetic disks and compressed rods

Savel’ev

Nori

2004

Phys. Rev. B

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Using the rigid magnetic vortex model, we develop a substantially modified Landau theory approach for analytically studying phase transitions between different spin arrangements in circular submicron magnetic dots subject to an in-plane externally-applied magnetic field. We introduce a novel order parameter: the inverse distance between the center of the circular dot and the vortex core. This order parameter is suitable for describing closed spin configurations such as curved or bent-spin structures and magnetic vortices. Depending on the radius and thickness of the dot as well as the exchange coupling, there are five different regimes for the magnetization reversal process when decreasing the in-plane magnetic field. The magnetization-reversal regimes obtained here cover practically all possible magnetization reversal processes. Moreover, we have derived the change of the dynamical response of the spins near the phase transitions and obtained a "critical slowing down" at the second order phase transition from the high-field parallel-spin state to the curved (C-shaped) spin phase. We predict a transition between the vortex and the parallel-spin state by quickly changing the magnetic field-providing the possibility to control the magnetic state of dots by changing either the value of the external magnetic field and/or its sweep rate. We study an illuminating mechanical analog (buckling instability) of the transition between the parallel-spin state and the curved spin state (i.e., a magnetic buckling transition). In analogy to the magnetic-disk case, we also develop a modified Landau theory for studying mechanical buckling instabilities of a compressed elastic rod embedded in an elastic medium. We show that the transition to a buckled state can be either first or second order depending on the ratio of the elasticity of the rod and the elasticity of the external medium. We derive the critical slowing down for the second-order mechanical buckling transition.

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Section: B Novel Order Parameters To Describe Magnetic and Mechanicamentioning

confidence: 98%

Magnetic and mechanical buckling: Modified Landau theory approach to study phase transitions in micromagnetic disks and compressed rods

Savel’ev

Nori

2004

Phys. Rev. B

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“…The released disk is compressed and an estimate based on the theory of elastic stability 18 shows that buckling should occur when the radius of the undercut exceeds 6 m ͑calculated for the built-in stress and thickness of our film͒. The asymmetry of the real system in the vertical direction may provide earlier buckling 19 and also leads to preferential upbuckling, preventing the released membrane from snapping into the substrate. The total timing of the wet etch determines the outer diama͒ Electronic…”

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confidence: 99%

Shell-type micromechanical actuator and resonator

Zalalutdinov

Aubin

Reichenbach

et al. 2003

Applied Physics Letters

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Dome-shaped radio-frequency micromechanical resonators were fabricated by utilizing the buckling of a prestressed thin polysilicon film. The enhanced rigidity of the dome structure leads to a significant increase of its resonant frequency compared to a flat plate resonator. The shell-type geometry of the structure also provides an imbedded actuation mechanism. Significant out-of plane deflections are actuated by mechanical stress introduced within the plane of the shell. We demonstrate that thermomechanical stress generated by a focused laser beam, or microfabricated resistive heater, provides an effective and fast mechanism to operate the dome as an acoustic resonator in the radio-frequency range. All-optical operation of the shell resonator and an integrated approach are discussed. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1622792͔ High-frequency microelectromechanical systems ͑MEMS͒ are widely considered as an element base for signal processing in the next generation of wireless communication devices. 1-3 Parametric amplification, 4,5 limit cycle oscillations, 6 and injection locking 7 demonstrated for MEMS oscillators allows one to build active circuits where signal processing would be implemented in the mechanical domain. However, a transduction mechanism for the effective conversion between the electrical and mechanical forms of the signal remains one of the key problems in MEMS design. The widely used capacitive drive 8 imposes restrictions related to cross talk issues and to high voltages required for actuation. Piezoelectric 9 or magnetomotive 10 actuation cannot be readily integrated because of the requirement for integrated circuit ͑IC͒-incompatible materials or high magnetic fields.In this letter, we demonstrate a design for a rf MEMS resonator based on the geometry of a shallow segment of a thin spherical shell. The finite curvature of the shell introduces an imbedded actuation mechanism by coupling the in-plane stress to the out-of-plane deflection of the shell. 11 The key feature of the shell actuation mechanism described in this letter is the local nature of the driving stress introduced at a specific point of the shell. A similar approach is employed in the design of macroscopic induced-strain actuators, 12,13 for ''smart structures'' actuated by small piezoelectric patches, surface bonded on a cylindrical shell at certain locations.In our micromechanical shell actuator, the in-plane strain is provided by stress introduced directly inside the shell layer. In our experiments we employ thermoelastic stress created by heating of the shell either by using a focused laser beam or a microfabricated heater. Using local heating, one can actuate cantilevering shell or bowl-type structures ͑shells supported at the center point͒. In the latter case, the compressive stress applied in the hoop direction close to the free edge of the shell flattens the bowl and provides a vertical component to the deflection of the periphery. The resulting motion can be complicated; thus for the configuration cons...

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“…Where comparably sized electro-thermal actuators require temperatures greater than 1000 • C [2], similar deflections can be achieved through buckling at temperatures of less than 100 • C. This amplification allows relatively low temperature increases from the heat source to efficiently drive the actuation mechanism in the adaptive valve. The buckling instability of microfabricated beams has been previously investigated by McCarthy et al [3], Carr and Wybourne [4] and Chiao and Lin [5] where beams were compressed and buckled under various loading mechanisms.…”

Section: Introductionmentioning

confidence: 98%