Dynamic response of plates resting on a fractional viscoelastic foundation and subjected to a moving load

Praharaj, R. K.; Datta, N.

doi:10.1080/15397734.2020.1776621

Cited by 29 publications

(7 citation statements)

References 34 publications

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“…In the beginning of 1930s, fractional derivative was introduced for describing the constitutive relation of some beam materials [16], and after 1980s, since fractional order equations have good memory and can be used to describe material properties more accurately with fewer parameters, they are considered to be good mathematical models for describing the dynamic mechanical behavior of materials [17]. In [18], the dynamic behavior of the thin plates resting on a fractionally damped viscoelastic foundation subjected to a moving point load is investigated and results show that the damping of the foundation system increases with increasing the order of the fractional derivative, which leads to a decrease in the dynamic response. In [19], the dynamic response spectra of fractionally damped viscoelastic beams subjected to concentrated moving load are presented and results reveal that with an increase in the order of the fractional derivative, the system damping of the system increases and the dynamic amplification factor (DAF) decreases, especially in the dynamic zone of the sweep parameter.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam $^{*}$

Yildirim

Alkan

2021

Journal of Mathematics

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In this paper, dynamic response analysis of a forced fractional viscoelastic beam under moving external load is studied. The beauty of this study is that the effect of values of fractional order, the effect of internal damping, and the effect of intensity value of the moving force load on the dynamic response of the beam are analyzed. Constitutive equations for fractional order viscoelastic beam are constructed in the manner of Euler–Bernoulli beam theory. Solution of the fractional beam system is obtained by using Bernoulli collocation method. Obtained results are presented in the tables and graphical forms for two different beam systems, which are polybutadiene beam and butyl B252 beam.

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Section: Introductionmentioning

confidence: 99%

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam $^{*}$

Yildirim

Alkan

2021

Journal of Mathematics

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“…The second large group of papers concerns the harmonic forced vibrations, both linear [155,[214][215][216] and geometrically nonlinear [217][218][219][220][221][222][223][224][225][226][227][228][229]. The other group of contributions focuses on the vibrations forced by a moving load or a moving mass, e.g., [193,[230][231][232].…”

Section: Structural Elements On Viscoelastic Foundationsmentioning

confidence: 99%

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Lewandowski,

Litewka,

Łasecka-Plura

et al. 2023

Buildings

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The paper is devoted to a review of recent achievements in the field of dynamic analysis of structures and structural elements, such as beams and plates, with embedded viscoelastic (VE) dampers and/or layers. The general characteristics of VE materials, their rheological models, and methods of parameters identification are discussed. New formulations of dynamic problems for systems with VE elements are also reviewed. The methods of determination of dynamic characteristics, together with the methods of analysis of steady-state and transient vibrations of such systems, are also discussed. Both linear and geometrically non-linear vibrations are considered. The paper ends with a review of the methods of sensitivity and uncertainty analysis, and the methods of optimization, for structures with VE elements.

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“…Some applications of fractional calculus in mechanics can be found in [31]. Moreover, the free, steady and transient vibration of beams, frame structures and plates where the fractional models are used to describe damping properties of systems materials are, among others, presented in [1,5,25,[32][33][34][35][36][37][38]. Some useful reviews papers which presented the application of fractional calculus in mechanics are [39][40][41].…”

Section: Description Of Nonlinear Vibration Of Beamsmentioning

confidence: 99%

Nonlinear steady state vibrations of beams made of the fractional Zener material using an exponential version of the harmonic balance method

Lewandowski

2022

Meccanica

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This paper presents the application of an exponential version of the harmonic balance method to the analysis of steady state vibration of geometrically nonlinear systems. A detailed description of the method and of the corresponding numerical procedure is provided. The von Karman theory is used to describe the effects of geometric nonlinearity. The material of the beams is modelled with the help of the Zener model using the fractional calculus. The problem is solved using an exponential version of the harmonic balance method. In the above-mentioned version, the complex calculus is used in contrast to the ordinary harmonic balance method, where the steady state vibrations are described with the help of the trigonometric functions. It significantly simplifies derivation of the amplitude equations. Moreover, the exponential version of the harmonic balance method is more elegant in comparison with the ordinary one. A detailed derivation of the amplitude equations is presented. The modified continuation method is proposed to solve the nonlinear amplitude equations and to determine the response curves. Moreover, the results of the exemplary calculation are presented and compared with known results in order to justify the efficiency and the correctness of the proposed approach.

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Dynamic response of plates resting on a fractional viscoelastic foundation and subjected to a moving load

Cited by 29 publications

References 34 publications

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam $^{*}$

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam $^{*}$

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Nonlinear steady state vibrations of beams made of the fractional Zener material using an exponential version of the harmonic balance method

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Dynamic response of plates resting on a fractional viscoelastic foundation and subjected to a moving load

Cited by 29 publications

References 34 publications

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam ∗

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam ∗

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Nonlinear steady state vibrations of beams made of the fractional Zener material using an exponential version of the harmonic balance method

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Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam $^{*}$

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam $^{*}$