Transient vibrations of a fractional Kelvin-Voigt viscoelastic cantilever beam with a tip mass and subjected to a base excitation

Freundlich, Jan

doi:10.1016/j.jsv.2018.09.006

Cited by 46 publications

(37 citation statements)

References 37 publications

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“…It can be shown that the drift part K 2r (t) is numerically much smaller than K 1r (t) and that it diminishes with time, so it can be neglected with only a slight loss in accuracy [43]. Thus it will not be considered here, leaving only the rst term.…”

Section: Determining the Impulse Responsementioning

confidence: 99%

“…However, to the best of authors' knowledge there is no exact solution to the herein analysed problem in literature. For this reason, the proposed solution will be validated for a special case whith only one mass attached to the tip of the beam, since in [43] Freundlich presented the exact analytical solution for this problem.…”

Section: Validation Of the Proposed Approximate Solutionmentioning

confidence: 99%

“…The literature on this problem is sparse and some of the papers are considering elastic [40] and fractional viscoelastic beam models [41,42]. Freundlich [43] analyzed the vibration of the fractional Kelvin-Voigt cantilever beam with base excitation and tip mass at the free end. The author used the separation of variables method and found the exact eigenvalues and eigenfunctions of the problem.…”

Section: Introductionmentioning

confidence: 99%

“…The presented approach is a step forward in investigation of this type of problems. The obtained solution is validated for a special case against the exact solution from [43] and numerical nite element method. The observed theoretical problem and the developed solution methods possess good potential for future use in energy harvesting devices with fractional damping considered.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation

Paunović

Cajić

Karličić

et al. 2019

Journal of Sound and Vibration

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The Galerkin method is widely applied for nding approximate solutions to vibration problems of beam and plate structures and for estimating their dynamic behaviour. Most studies employ the Galerkin method in the analysis of the undamped systems, or for simple structure models with viscous damping. In this paper, a novel approach of using the Galerkin method and Fourier transform to nd the solution to the problem of vibration of fractionally damped beams with an arbitrary number of attached concentrated masses and base excitation is presented. The considered approach is novel and it lends itself to determination of the impulse response of the beam and leads to the solution of the system of coupled fractional order dierential equations. The proposed approximate solution is validated against the exact solution for a special case with only one tip mass attached, as well as against the Finite Element Method Solution for a special case with classical viscous damping model. Numerical analysis is also given, including the examples of vibration analysis of viscoelastic beams with dierent fractional derivative orders, retardation times, and the number, weight and position of the attached masses.

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Section: Determining the Impulse Responsementioning

confidence: 99%

Section: Validation Of the Proposed Approximate Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation

Paunović

Cajić

Karličić

et al. 2019

Journal of Sound and Vibration

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show abstract

“…Fractional-damping models can be employed both for structures and their foundations. Mostly, they have been employed to investigate structures (Freundlich 2019(Freundlich , 2016Shitikova 2006, 2011;Asgari et al 2017;Datta 2020a, 2020b;Praharaj et al 2020). Kang Xu et al proposed a fractional-order proportional derivative controller to contain the large-amplitude earthquake-induced vibrations of buildings (Xu et al (2020)).…”

Section: Introductionmentioning

confidence: 99%

On the transient response of plates on fractionally damped viscoelastic foundation

Praharaj

Datta

2020

Comp. Appl. Math.

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This work underlines the importance of the application of fractional-order derivative damping model in the modelling of the viscoelastic foundation, by demonstrating the effect of various orders of the fractional derivative on the dynamic response of plates resting on the viscoelastic foundation, subjected to concentrated step load. The foundation of the plate is modelled as a fractionally-damped Kelvin-Voigt model. Modal superposition method and Triangular strip matrix approach are used to solve the partial fractional differential equations of motion. The influence of (a) fractional-order derivative, (b) foundation stiffness, and (c) foundation damping viscosity parameter on the dynamic response of the plate are investigated. Theoretical results show that with the increase in the order of derivative, the damping of the system increases, which leads to decreased dynamic response. The results obtained from the fractional-order damping model and integer-order damping model are compared. The results are verified with literature and numerical results (ANSYS).

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A note on analytical solutions for vibrations of beams with an attached large mass

Manolis

2022

Arch Appl Mech

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Transient vibrations of a fractional Kelvin-Voigt viscoelastic cantilever beam with a tip mass and subjected to a base excitation

Cited by 46 publications

References 37 publications

A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation

A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation

On the transient response of plates on fractionally damped viscoelastic foundation

A note on analytical solutions for vibrations of beams with an attached large mass

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