Response of viscoelastic damping system modeled by fractional viscoelastic oscillator

Zl, Li; Sun, DG; Han, BH; Sun, Bao; Zhang, X; Meng, Jie; Fx, Liu

doi:10.1177/0954406216642477

Cited by 6 publications

(4 citation statements)

References 13 publications

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“…Recently, there has been much interest in the use of fractional differential calculus to explain and model many physical phenomena. For example, fractional differential calculus has been used to design and/or model PI λ D µ controllers, heat conduction [23][24][25], thermoelasticity [26], complex nonlinear systems [7], supercapacitors, electrical and mechanical systems [27][28][29], electrical filters, dielectric relaxation, diffusion, and viscoelasticity [30].…”

Section: Mathematical Modelmentioning

confidence: 99%

Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach

Błasiak

2021

Energies

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This article presents a variable-order derivative (VOD) time fractional model for describing heat transfer in the rotor or stator in non-contacting mechanical face seals. Most theoretical studies so far have been based on the classical equation of heat transfer. Recently, constant-order derivative (COD) time fractional models have also been used. The VOD time fractional model considered here is able to provide adequate information on the heat transfer phenomena occurring in non-contacting face seals, especially during the startup. The model was solved analytically, but the characteristic features of the model were determined through numerical simulations. The equation of heat transfer in this model was analyzed as a function of time. The phenomena observed in the seal include the conduction of heat from the fluid film in the gap to the rotor and the stator, followed by convection to the fluid surrounding them. In the calculations, it is assumed that the working medium is water. The major objective of the study was to compare the results of the classical equation of heat transfer with the results of the equations involving the use of the fractional-order derivative. The order of the derivative was assumed to be a function of time. The mathematical analysis based on the fractional differential equation is suitable to develop more detailed mathematical models describing physical phenomena.

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Section: Mathematical Modelmentioning

confidence: 99%

Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach

Błasiak

2021

Energies

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“…According to different background, there are several definitions of the fractional-order derivative, 46,47 and under some special conditions, they are equivalent. In this study, the Caputo definition is adopted with the following form…”

Section: Nanobeam Model Based On Nonlocal Continuum Approachmentioning

confidence: 99%

Mathematical modeling of a fractionally damped nonlinear nanobeam via nonlocal continuum approach

Jha

Dasgupta

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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Modeling of fractionally damped nanostructure is extremely important because of its inherent ability to capture the memory and hereditary effect of several viscoelastic materials extensively used in nanotechnology. The nonlinear free vibration characteristics of a simply-supported nanobeam with fractional-order derivative damping via nonlocal continuum theory are studied in this article. Using Newton’s second law, the equation of motion for the nanobeam embedded in a viscoelastic matrix is derived. The Galerkin method is employed to transform the integro-partial differential equation of motion into a Duffing-type nonlinear ordinary differential equation. The fractional-order damping term is replaced by a combination of linear damping and linear stiffness term. The approximate analytical solution obtained via method of averaging is found to be in good agreement with solution obtained through numerical scheme. Detailed study of system parameters reveals that the fractional-order derivative damping has significant influence on the time response and effective natural frequency of the nanobeam.

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“…Reference [17] mentioned that Prony series could be applied to approximate numerical solutions of fractional-order models to any desired accuracy. Reference [18] proposed a fractional-order model that considered the geometric factors of viscoelastic damping system, and a numerical method was derived on the basis of matrix function theory and the Grumwald-Letnikov discrete form of fractional derivative to study the vibration response of viscoelastic suspension installed on heavy tracked vehicles. Reference [19] studied the fractional Maxwell model based on the generalized Caputo definition of fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic Fractional Model Based on Harmonic Excitation

Chen

et al. 2022

Mathematical Problems in Engineering

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This paper analyzes the viscoelastic fractional constitutive model based on the analytical form of the fractional derivative of the sine (cosine) function. First, the polynomials of the linear model are combined into a fractional derivative term, then the complex modulus can be easily obtained, and the response characteristics of the model can be analyzed. Second, the fractional nonlinear model is expressed in harmonic form, which can easily identify nonlinear parameters. Finally, fractional-order nonlinear models can also be transformed into integer-order nonlinear forms. In this paper, the transformation model is verified by literature test data, which show the correctness and accuracy of the transformation form.

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Response of viscoelastic damping system modeled by fractional viscoelastic oscillator

Cited by 6 publications

References 13 publications

Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach

Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach

Mathematical modeling of a fractionally damped nonlinear nanobeam via nonlocal continuum approach

Viscoelastic Fractional Model Based on Harmonic Excitation

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