Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation

Freundlich, Jan

doi:10.1155/2013/126735

Cited by 33 publications

(13 citation statements)

References 18 publications

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“…Under the assumption of Bernoulli-Euler theory, the moment of inertia and shear deformation are neglected, the bending stiffness and mass density are assumed to be uniform [25], and the governing equation of the forced lateral motion of the beam is obtained. 4 4 2…”

Section: mentioning

confidence: 99%

A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams

Zhang

Chen

et al. 2019

Chaos, Solitons & Fractals

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In this paper, a new method is presented for solving the constitutive equations of fractional-order viscoelastic Euler-Bernoulli beams. Firstly, the constitutive equation of the Euler-Bernoulli beam is established by analyzing the constitutive relation between the fractional viscoelastic materials. Secondly, the constitutive equation of the beam is transformed into a matrix equation by using a Quasi-Legendre polynomial in the time domain. Then the matrix equation is discretized and solved, and the numerical solution is obtained for the constitutive equation of the beam. Finally, numerical analysis of two different fractional viscoelastic materials is carried out by numerical experiments. Displacements under different external loads are obtained for the polybutadiene beam and butyl B252 beam. With the change of time and position, the change law of displacements is found. And the performance of the two materials is compared and analyzed.

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Section: mentioning

confidence: 99%

A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams

Zhang

Chen

et al. 2019

Chaos, Solitons & Fractals

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“…The base excitation of beams is another interesting problem for analysis due to recent application for energy harvesting purposes [39]. 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.…”

Section: Introductionmentioning

confidence: 99%

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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“…Freundlich, in paper [7], is studying the vibration of a simply supported beam with a viscoelastic behavior of fractional order. The beam, considering the Bernoulli-Euler hypotheses, was excited by the supports movement.…”

Section: Introductionmentioning

confidence: 99%

Hysteretically Symmetrical Evolution of Elastomers-Based Vibration Isolators within α-Fractional Nonlinear Computational Dynamics

2019

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This study deals with computational analysis of vibration isolators' behavior, using the fractional-order differential equations (FDE). Numerical investigations regarding the influences of α-fractional derivatives have been mainly focused on the dissipative component within the differential constitutive equation of rheological model. Two classical models were considered, Voigt-Kelvin and Van der Pol, in order to develop analyses both on linear and nonlinear formulations. The aim of this research is to evaluate the operational capability, provided by the α-fractional derivatives within the viscous component of certain rheological model, to enable an accurate response regarding the realistic behavior of elastomeric-based vibration isolators. The hysteretic response followed, which has to be able to assure the symmetry of dynamic evolution under external loads, and at the same time, properly providing dissipative and conservative characteristics in respect of the results of experimental investigations. Computational analysis was performed for different values of α-fractional order, also taking into account the integer value, in order to facilitate the comparison between the responses. The results have shown the serviceable capability of the α-fractional damping component to emulate, both a real dissipative behavior, and a virtual conservative characteristic, into a unitary way, only by tuning the α-order. At the same time, the fractional derivative models are able to preserve the symmetry of hysteretic behavior, comparatively, e.g., with rational-power nonlinear models. Thereby, the proposed models are accurately able to simulate specific behavioral aspects of rubber-like elastomers-based vibration isolators, to the experiments.

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Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation

Cited by 33 publications

References 18 publications

A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams

A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams

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

Hysteretically Symmetrical Evolution of Elastomers-Based Vibration Isolators within α-Fractional Nonlinear Computational Dynamics

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