Nonlinear vibration of beams and rectangular plates

Eisley, Joe G.

doi:10.1007/bf01602658

Cited by 188 publications

(77 citation statements)

References 7 publications

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“…This averaging procedure is characteristic of formulations based on stress or force functions [11], but equations (28) and (29) are not strictly the same as equations (27).…”

Section: Non-local Non-linear Modelmentioning

confidence: 99%

On displacement based non-local models for non-linear vibrations of thin nano plates

Chuaqui

Ribeiro

2018

MATEC Web Conf.

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Abstract. This paper addresses the formulation of displacement based, non-linear, plate models adopting Eringen's non-local elasticity, to study the modes of vibration of thin, nano plates. Plate models governed by ordinary differential equations of motion with generalized displacements as unknowns have some advantages over mixed type formulations, but difficulties arise in the development of such non-linear models when non-local effects are taken into account. To circumvent those difficulties, approximations of debatable justification can be imposed. Different approximations are discussed here and the accuracy of the best non-local, non-linear displacement based model achieved is put to test, by carrying out comparisons with a model based on Airy's stress function.

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“…This averaging procedure is characteristic of formulations based on stress or force functions [11], but equations (28) and (29) are not strictly the same as equations (27).…”

Section: Non-local Non-linear Modelmentioning

confidence: 99%

On displacement based non-local models for non-linear vibrations of thin nano plates

Chuaqui

Ribeiro

2018

MATEC Web Conf.

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“…SEM imaging and optical profilometry indicate that doubly supported beams, 15 μm and longer, are buckled up due to residual compressive stress in the device layer. In doubly supported beams, midplane stretching [55] leads to amplitudehardening in prebuckled beams [56] due to a nonlinear load- Deflection of the beam x changes the fraction of light absorbed, leading to self-oscillation in the first bending mode when the laser power is higher than a threshold value, P crit . Modulation of the reflected light is measured in a high-speed photodiode and used to transduce motion.…”

Section: Setup and Proceduresmentioning

confidence: 99%

Entrainment of Micromechanical Limit Cycle Oscillators in the Presence of Frequency Instability

Blocher

Zehnder

Rand

2013

J. Microelectromech. Syst.

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Abstract-The nonlinear dynamics of micromechanical oscillators are explored experimentally. Devices consist of singly and doubly supported Si beams, 200 nm thick and 35 μm long. When illuminated within a laser interference field, devices selfoscillate in their first bending mode due to feedback between laser heating and device displacement. Compressive prestress buckles doubly supported beams leading to a strong amplitude-frequency relationship. Significant frequency instability is seen in doubly supported devices. Self-resonant beams are also driven inertially with varying drive amplitude and frequency. Regions of primary, sub-, and superharmonic entrainment are measured. Statistics of primary entrainment are measured for low drive amplitudes, where the effects of frequency instability are measurable. Suband superharmonic entrainment are not seen in singly supported beams. A simple model is built to explain why high-order entrainment is seen only in doubly supported beams. Its analysis suggests that the strong amplitude-frequency relationship in doubly supported beams enables hysteresis, wide regions of primary entrainment, and high orders of sub-and superharmonic entrainment.[2012-0225]

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“…The nonlinear beam equation was proposed by Woinovsky-Krieger [13] (see also [6]) as a model for the transverse defection u of an extensible beam of natural length l, where ρ, κ, α and β are positive constants. In this article we study the initial value problem for the modified model of (1.1) proposed by Ball [2], where he assumes that the beam has linear structural (Kelvin-Voigt) and external (frictional) damping, that is, we consider the following problem:…”

Section: Introductionmentioning

confidence: 99%

Decay estimates for the Cauchy problem for the damped extensible beam equation

Racke

Yoshikawa

2015

Applicable Analysis

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The extensible beam equation proposed by Woinovsky-Krieger [13] is a fourth order dispersive equation with nonlocal nonlinear terms. In this paper we study the Cauchy problem of the extended model by Ball who proposed the following model with external and structural damping terms:For η > 0 this represents a Kelvin-Voigt damping. We show the unique global existence of solution for this problem and give a precise description of the decay of solutions in time.

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Nonlinear vibration of beams and rectangular plates

Cited by 188 publications

References 7 publications

On displacement based non-local models for non-linear vibrations of thin nano plates

On displacement based non-local models for non-linear vibrations of thin nano plates

Entrainment of Micromechanical Limit Cycle Oscillators in the Presence of Frequency Instability

Decay estimates for the Cauchy problem for the damped extensible beam equation

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