Stability of cantilever on elastic foundation under a subtangential follower force via shear deformation beam theories

Jiang, Zi-Cheng; Ma, Weili; Li, Xian-Fang

doi:10.1016/j.tws.2020.106853

Cited by 8 publications

(2 citation statements)

References 46 publications

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“…However, studies in this area are still limited. For example, Hosseini et al 16 conducted vibration studies on viscoelastic cantilever beams placed on nonlinear elastic foundations, while Jiang et al 17 investigated the structural instability of freely clamped rectangular and circular beams placed on Winkler foundations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic vibration analysis of cantilever beams on nonlinear fractional viscoelastic foundation under Gaussian white noise

Qu,

Cui,

Cui

et al. 2024

Preprint

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This paper presents the dynamic response of cantilever beam on fractional-order nonlinear viscoelastic foundation subjected to Gaussian white noise. The control equations of the cantilever beam on viscoelastic foundation are established using Hamilton’s principle. The problem is solved using the shifted Chebyshev polynomial algorithm, and the control equations are transformed into a system of nonlinear algebraic equations. Numerical examples analyse the correction error and the second norm error, confirming the effectiveness and accuracy of the algorithm in solving such problems. Furthermore, the algorithm’s robustness was verified by comparing the responses of Gaussian white noise and non-Gaussian white noise cantilever beam on the viscoelastic foundation. The study examined the impact of various loads and parameters on the cantilever beam, as well as the effect of different harmonic loads on its stress. The research results are in line with the existing literature. These studies offer valuable guidance for practical engineering and enhance comprehension of the dynamic response of cantilevers on foundation in complex environments.

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Section: Introductionmentioning

confidence: 99%

Dynamic vibration analysis of cantilever beams on nonlinear fractional viscoelastic foundation under Gaussian white noise

Qu,

Cui,

Cui

et al. 2024

Preprint

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“…They acquired the flutter instability threshold and resonant frequencies of the system with surface effects. Jiang et al 51 studied the static stability of an embedded clamped-free column subjected to a tangential load based on shear deformation beam theory. They evaluated the effects of system geometry and foundation parameters on the critical buckling load.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent vibrational behavior of embedded spinning tubes under gravitational load in hygro-thermo-magnetic fields

Liu

Ruonan

Koochakianfard

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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In the present investigation, with the aim of performance improvement of size-dependent bi-gyroscopic structures, the vibrational behavior of spinning small-scale tunes conveying fluid embedded in various foundations subjected to distributed tangential load and hygro-thermo-magnetic environments by including gravitational effect is investigated. The modified couple stress theory is used to study the microscale tube, and the modified nonlocal theory is utilized to model the nanoscale tubes. A parametric investigation is also conducted to highlight the impacts of various key factors such as gravity, flow profile modification factor, fluid velocity, spinning speed, substrate coefficients, boundary conditions, size-dependent parameters, and environmental attacks on divergence and flutter thresholds of the structure. The dynamical equations are solved using Laplace transformation as well as Galerkin discretization techniques, and forward and backward frequencies are identified accordingly. Meanwhile, the instability borders of the system are obtained analytically. Campbell and stability diagrams, and the time history of the system, are acquired. The results revealed that contrary to influences of gravity, magnetization, and size-dependent parameters, the compressive tangential load and humidity have decreasing effects on the vibrational frequencies and make the system prone to experience static and dynamical instabilities. Moreover, it is determined that applying the viscous foundation eliminates the re-stabilization zone in the system stability evolution, and after the occurrence of the divergence phenomenon, the system immediately undergoes the flutter instability.

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On the mechanical behavior of two directional symmetrical functionally graded beams under moving load

Abdelrahman

Mohamed

Alshorbagy

et al. 2021

Int J Mech Mater Des

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Stability of cantilever on elastic foundation under a subtangential follower force via shear deformation beam theories

Cited by 8 publications

References 46 publications

Dynamic vibration analysis of cantilever beams on nonlinear fractional viscoelastic foundation under Gaussian white noise

Dynamic vibration analysis of cantilever beams on nonlinear fractional viscoelastic foundation under Gaussian white noise

Size-dependent vibrational behavior of embedded spinning tubes under gravitational load in hygro-thermo-magnetic fields

On the mechanical behavior of two directional symmetrical functionally graded beams under moving load

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