On dynamic snap buckling of shallow arches.

Humphreys, John Stirling

doi:10.2514/3.3561

Cited by 105 publications

(40 citation statements)

References 7 publications

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“…4(b). The governing equation for an arch-shaped beam under a distributed load is given as follows [6], [7], [9], [11], [12]:…”

Section: Arch-shaped Beam Under An Electrostatic Loadingmentioning

confidence: 99%

“…The governing equations of those studies [6], [7], [9], [11], [12] are for dynamics of an arch-shaped beam. Here, only the static response is studied, and therefore, (5) truncates those time-related terms.…”

Section: Arch-shaped Beam Under An Electrostatic Loadingmentioning

confidence: 99%

“…where the α i 's (i = 1 to 3) are defined as follows: For the convenience of computation, (8) is written in the following form as Humphreys did [6]:…”

Section: Arch-shaped Beam Under An Electrostatic Loadingmentioning

confidence: 99%

See 2 more Smart Citations

Snap-Through and Pull-In Instabilities of an Arch-Shaped Beam Under an Electrostatic Loading

Yin¹,

Wang

et al. 2007

J. Microelectromech. Syst.

106

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Abstract-The snap-through and pull-in instabilities of the micromachined arch-shaped beams under an electrostatic loading are studied both theoretically and experimentally. The pull-in instability that results in a system collision with an electrode substrate may lead to a system failure and, thus, limits the system maximum displacement. The beam/plate structure with a flat initial configuration under an electrostatic loading can only experience the pull-in instability. With the different arch configurations, the structure may experience either only the pull-in instability or the snap-through and pull-in instabilities together. As shown in our computation and experiment, those arch-shaped beams with the snap-through instability have the larger maximum displacement compared with the arch-shaped beams with only the pull-in stability and those with the flat initial configuration. The snapthrough occurs by exerting a fixed load, and the structure experiences a discontinuous displacement jump without consuming power. Furthermore, after the snap-through jump, the structures are demonstrated to have the capacity to withstand further electrostatic loading without pull-in. Those properties of consuming no power and increasing the structure deflection range without pull-in is very useful in microelectromechanical systems design, which can offer better sensitivity and tuning range.

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“…4(b). The governing equation for an arch-shaped beam under a distributed load is given as follows [6], [7], [9], [11], [12]:…”

Section: Arch-shaped Beam Under An Electrostatic Loadingmentioning

confidence: 99%

Section: Arch-shaped Beam Under An Electrostatic Loadingmentioning

confidence: 99%

See 1 more Smart Citation

Snap-Through and Pull-In Instabilities of an Arch-Shaped Beam Under an Electrostatic Loading

Yin¹,

Wang

et al. 2007

J. Microelectromech. Syst.

106

View full text Add to dashboard Cite

show abstract

“…Figure 3 compares the displacement response predicted in the present study with the results of Bathe et al [4], Humphreys [5], Noor and Knight [6]. In that figure, the deflection ratio  , the time parameter  , and the load parameter P are defined as:…”

Section: Numerical Examplementioning

confidence: 97%

Geometric Nonlinear Analysis for Frame Structures, Part 2: Dynamic Analysis

Jin¹,

Li²

2017

Proceedings of the 2017 6th International Conference on Energy and Environmental Protection (ICEEP 2017)

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Abstract:In this paper, the governing equation of dynamic analysis for frame structures is derived, with geometric nonlinearity considered. In the process of derivation, the updated Lagrange format is adopted and the elemental equilibrium equation is established at current configuration and then transformed into the initial configuration. To simplify the calculation of mass matrix, it is assumed that the beam's mass is only related with its rigid configuration. In other words, the mass effect due to the beam's deformation is ignored. Finally, a numerical example about dynamic buckling analysis of a circular arch subjected to a uniformly distributed step load is presented and discussed detailedly, demonstrating the validity and accuracy of the present method.

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“…This is called "dynamic pull-in", which characterizes the instability of the structure due to dynamics considerations. Snap-through of arches during their transient motion under uniform dynamic pressure loading has been reported in [26]. The fact that snap-through motion can be triggered by means of dynamic loading allows us to define "dynamic snap-through" which means snap-through due to dynamic effects.…”

Section: Bistable Behavior Of a Shallow Archmentioning

confidence: 99%

An Electrostatically Actuated MEMS Arch Band-Pass Filter

Ouakad

2013

Shock and Vibration

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Abstract. This work presents an investigation of the dynamics of micromachined arches resonators and their potential to be utilized as band-pass filters. The arches are actuated by a DC electrostatic load superimposed to an AC harmonic load. The dynamic response of the arch is studied analytically using a Galerkin-based reduced-order model when excited near its fundamental and third natural frequencies. Several simulation results are presented demonstrating interesting jumps and snap-through behavior of the arches and their attractive features for uses as band-pass filters, such as their sharp roll-off from pass bands to stop bands and their flat response.

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On dynamic snap buckling of shallow arches.

Cited by 105 publications

References 7 publications

Snap-Through and Pull-In Instabilities of an Arch-Shaped Beam Under an Electrostatic Loading

Snap-Through and Pull-In Instabilities of an Arch-Shaped Beam Under an Electrostatic Loading

Geometric Nonlinear Analysis for Frame Structures, Part 2: Dynamic Analysis

An Electrostatically Actuated MEMS Arch Band-Pass Filter

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