Stability of the Bernoulli–Euler Beam in Coupled Electric and Thermal Fields

Морозов, Н. Ф.; Indeitsev, D. A.; Лукин, А. В.; Popov, I. A.; Privalova, O. V.; Shtukin, L. V.

doi:10.1134/s1028335818080086

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…Во-первых, коэффициенты (47) пропорциональны интенсивности лазерного излучения. Во-вторых, названные коэффициенты зависят от геометрических характеристик резонатора (от размеров области, в которой решается тепловая задача) -а значит, от параметра внутренней частотной расстройки σ ω , определяющего близость к внутреннему резонансу (29):…”

Section: дискретизация континуальной системы методом галёркинаunclassified

“…В более ранних работах [29][30][31] рассматривалась динамика и упругая устойчивость балочного элемента МЭМС и НЭМС при кратковременных тепловых воздействиях. В [32] был исследован характер свободных продольно-изгибных колебаний стержня в случае внутреннего комбинационного резонанса между двумя изгибными и низшей продольной формами колебаний.…”

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“…При этом задача рассматривается в связанной продольно-изгибной постановке, и одним из предметов исследования является влияние фактора продольных колебаний на динамику системы. Рассматриваемый случай внутреннего резонанса записывается как 2ω l ωn , (29) где ω l -некоторая из частот изгибных колебаний, ωn -некоторая из частот продольных колебаний. Уравнение малых свободных продольных колебаний в принятых обозначениях имеет вид u = 12β 2 ü.…”

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Nonlinear modal interaction between longitudinal and bending vibrations of a beam resonator under periodic thermal loading

Морозов¹,

Indeitsev²,

Lukin³

et al. 2022

Vestnik SPbSU. Mathematics. Mechanics. Astronomy

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The paper investigates the nonlinear modal interaction of longitudinal and bending vibrations of a beam resonator under periodic thermal loading. The mode of parametric oscillations is investigated under conditions of internal multiple resonance between some flexural and longitudinal forms of free oscillations of the resonator. The possibility of generation in the system of the longitudinal-bending mode was found, the frequency of the slow envelope of which essentially depends on the parameter of the internal frequency detuning, which is directly related to the magnitude of external disturbances subject to high-precision measurement.

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Section: дискретизация континуальной системы методом галёркинаunclassified

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Nonlinear modal interaction between longitudinal and bending vibrations of a beam resonator under periodic thermal loading

Морозов¹,

Indeitsev²,

Lukin³

et al. 2022

Vestnik SPbSU. Mathematics. Mechanics. Astronomy

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“…In a recent study, Morozov et al [33] explored the effects of initial curvature amplitude and shape on static equilibrium positions under electrostatic and thermal influences, utilizing a geometrically nonlinear model of a Bernoulli-Euler beam. Additionally, the same research group [34] employed numerical methods and bifurcation-based theory, considering both symmetric and asymmetric lower modes of free vibrations, to investigate the potential use of these structures as sensitive elements in high-precision mode-localized resonant microaccelerometers.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Structural Analysis of MEMS Shallow Arch Assuming Multimodal Initial Curvature Profiles

Alneamy,

Ouakad

2024

Mathematics

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The present investigation focuses on the design and mathematical modeling of a microelectromechanical (MEMS) mode-localized based sensor/actuator system. This device incorporates a sensitive clamped–clamped shallow arch microbeam with an initial curvature shaped to resemble one of the first two symmetric and asymmetric modes of free oscillations of a clamped–clamped beam. The analysis reveals that with a suitable arrangement of the initial shape of the device flexible electrode and a proper tuning of the maximum initial rise and the actuating dc load enables the transition to display certain bistable behavior. This could be a better choice to build a device with a large stroke. Furthermore, the generated data showed the occurrence of mode-veering, indicating a coupling between the concerned symmetric and asymmetric modes of vibrations, and offering the possibility for such a device to be used as a mode-localized MEMS-based sensor utilizing veering and crossing phenomena. Indeed, where a certain energy is exchanged between symmetric and asymmetric modes of a microbeam, it can be utilized to serve as a foundation for the development of a new class of highly precise resonant sensors that can capture, with a certain level of precision, any of the sensed signal amplitudes.

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Internal resonance between transverse vibration modes of a 2D material nanostrip under laser opto-thermal excitation

Morozov,

Lukin,

Popov

et al. 2024

Nonlinear Dyn

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Stability of the Bernoulli–Euler Beam in Coupled Electric and Thermal Fields

Cited by 10 publications

References 12 publications

Nonlinear modal interaction between longitudinal and bending vibrations of a beam resonator under periodic thermal loading

Nonlinear modal interaction between longitudinal and bending vibrations of a beam resonator under periodic thermal loading

Modeling and Structural Analysis of MEMS Shallow Arch Assuming Multimodal Initial Curvature Profiles

Internal resonance between transverse vibration modes of a 2D material nanostrip under laser opto-thermal excitation

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