Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Ali, Sajid

doi:10.1002/mma.8965

Cited by 2 publications

(2 citation statements)

References 59 publications

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“…The impact of the time-dependent longitudinal velocity of nanobeams on the frequencies was studied by Rezaee et al [32] and Liu et al [33,34]. Dynamic responses of micro/nano moving beams were considered in several recent studies [35][36][37]. The impact of thermal conditions on the vibration and stability of a microbeam was thoroughly studied in [35].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Characteristics of a Small-Size Beam Mounted on an Accelerating Structure

Ali

Hawwa

2023

Micromachines

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This study focuses on the nonlinear vibration of a small-size beam hosted in a high-speed moving structure. The equation of the beam’s motion is derived using the coordinate transformation. The small-size effect is introduced by applying the modified coupled stress theory. The equation of motion involves quadratic and cubic terms due to mid-plane stretching. Discretization of the equation of motion is achieved via the Galerkin method. The impact of several parameters on the non-linear response of the beam is investigated. Bifurcation diagrams are used to investigate the stability of the response, whereas softening/hardening characteristics of the frequency curves are used as an indication of nonlinearity. Results indicate that increasing the magnitude of the applied force tends to signify the nonlinear hardening behavior. In terms of the periodicity of the response, at a lower amplitude of the applied force, the response appears to be a one-period stable oscillation. Increasing the length scale parameter, the response moves from chaotic to period-doubling to the stable one-period response. The impact of the axial acceleration of the moving structure on the stability as well as on the nonlinearity of the response of the beam is also investigated.

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Section: Introductionmentioning

confidence: 99%

“…Dynamic responses of micro/nano moving beams were considered in several recent studies [35][36][37]. The impact of thermal conditions on the vibration and stability of a microbeam was thoroughly studied in [35]. A stability analysis of the response was performed through the bifurcation diagrams.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics of a Small-Size Beam Mounted on an Accelerating Structure

Ali

Hawwa

2023

Micromachines

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Study of the dynamic process in a nonlinear mathematical model of the transverse oscillations of a moving beam under perturbed boundary conditions

Slipchuk,

Pukach,

Vovk

et al. 2024

Math. Model. Comput.

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The study of transverse oscillations of systems moving along their axis is a very difficult, but at the same time a very important task. Mathematical models of nonlinear transverse oscillations of a beam moving along its axis are analyzed in this paper work, both for non-resonant and resonant cases. The task becomes even more complicated if we additionally take into account the method of fastening the ends of the beam or the perturbation at its ends. We have obtained dependencies that can be used in construction, transport, industry, mechanical engineering and other domains of technology, ensuring the stability and safety of the operation of such mechanical systems. Mathematical models have been obtained for structural engineers to determine the amplitude–frequency response of relevant structures. These mathematical models are key to researching the dynamics of moving media. The obtained results allow considering not only the influence of kinematic and physical-mechanical parameters on the amplitude–amplitude frequency response of the medium, but also the fastening method. In addition, the correlations obtained in the paper make it possible to study not only the influence of the moving medium parameters on the nature of changes in the frequency and amplitude of oscillations, but also to consider the movement at the points of support of the medium. Namely, even at the stage of designing a pipeline for a liquid flowing at a certain speed, it is possible to consider the influence of the oscillation of the supports or their fastening method on the dynamics of the oscillatory process. The resulting dependencies allow designers to consider the influence of the characteristics given in the paper with a high level of accuracy and predict dynamic phenomena in them. In engineering calculations of various mechanical systems, the resulting dependencies can be used to optimize parameters to avoid negative destructive phenomena during operation.

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Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Cited by 2 publications

References 59 publications

Dynamic Characteristics of a Small-Size Beam Mounted on an Accelerating Structure

Dynamic Characteristics of a Small-Size Beam Mounted on an Accelerating Structure

Study of the dynamic process in a nonlinear mathematical model of the transverse oscillations of a moving beam under perturbed boundary conditions

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