Journal ArticleDOI
Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials
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In this paper, three simple constitutive relationships for application to viscoelastic materials are studied for both a rubbery and a glassy visco-elastic material are fit by the three schemes.Abstract:
Three simple constitutive relationships are studied for application to viscoelastic materials. Experimental results for both a rubbery and a glassy viscoelastic material are fit by the three schemes. The Kelvin-Voigt scheme is shown to be adequate in only limited frequency ranges. A three-parameter fractional order constitutive relationship provides a substantially better model over a much larger bandwidth. A four-parameter fractional model improves on the accuracy in materials with significant glassy regionsread more
Citations
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Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results
TL;DR: In this article, the authors present the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics.
Journal ArticleDOI
Identification of the parameters of the Kelvin-Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers
TL;DR: In this paper, a family of methods for identification of the parameters of both the Kelvin-Voigt fractional model and the Maxwell fractional models are presented in order to describe the behavior of viscoelastic dampers using a small number of parameters.
Journal ArticleDOI
Research and applications of viscoelastic vibration damping materials: A review
TL;DR: A comprehensive review of the various research methods and theory calculation models that are employed in engineering to study the static and dynamic vibration characteristics of viscoelastic damping material (VDM) formed structures is presented in this article.
Journal ArticleDOI
Continuous graded Gyroid cellular structures fabricated by selective laser melting: Design, manufacturing and mechanical properties
Lei Yang,Lei Yang,Raya Mertens,Massimiliano Ferrucci,Chunze Yan,Yusheng Shi,Shoufeng Yang,Shoufeng Yang +7 more
TL;DR: In this article, graded gyroid cellular structures (GCSs) with varying gradient directions were designed and manufactured via selective laser melting (SLM), and the surface morphology and mechanical response of these structures under compressive loads were investigated.
References
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Journal ArticleDOI
On the Fractional Calculus Model of Viscoelastic Behavior
Ronald L. Bagley,Peter J. Torvik +1 more
TL;DR: In this paper, a mathematical model of the viscoelastic phenomenon employing derivatives of fractional order is examined in light of its consistency with thermodynamic principles, which leads the model to predict realistic sinusoidal response as well as realistic relaxation and creep responses.
Journal ArticleDOI
Fractional calculus in the transient analysis of viscoelastically damped structures
Ronald L. Bagley,Peter J. Torvik +1 more
TL;DR: In this article, the authors used fractional calculus to model the viscoelastic behavior of a damping layer in a simply supported beam and analyzed the beam by using both a continuum formulation and a finite element formulation to predict the transient response to a step loading.
Book ChapterDOI
A brief history and exposition of the fundamental theory of fractional calculus
TL;DR: A case study of mathematical growth is given in this articleocusing on the origin and development of a mathematical idea from its birth in intellectual curiosity to applications, and the possibilities for the use of fractional calculus in applicable mathematics.
Journal ArticleDOI
Computational algorithms for FE formulations involving fractional operators
TL;DR: In this paper, transient solution algorithms for finite element simulations of viscoelastic problems involving fractional integrodifferential operators are developed for the Grunwald-Liouville-Riemann formalism.
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