Designing of Dynamic Spectrum Shifting in Terms of Non-Local Space-Fractional Mechanics

Krzysztof Szajek; Wojciech Sumelka; Krzysztof Bekus; Tomasz Błaszczyk

doi:10.3390/en14020506

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Title

Designing of Dynamic Spectrum Shifting in Terms of Non-Local Space-Fractional Mechanics

Authors

Krzysztof Szajek (WILiT) ^{[ 1 ][ 2.7 ][ P ]}
Wojciech Sumelka (WILiT) ^{[ 1 ][ 2.7 ][ P ]}
Krzysztof Bekus
Tomasz Błaszczyk

^{[ 1 ]} Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | ^{[ P ]} employee

Scientific discipline (Law 2.0)

[2.7] Civil engineering and transport

Year of publication

2021

Published in

Energies

Journal year: 2021 | Journal volume: vol. 14 | Journal number: no. 2

Article type

scientific article

Publication language

english

Keywords

EN

discrete model
continuum non-local model
fractional calculus
fractional mechanics

Abstract

EN In this paper, the applicability of the space-fractional non-local formulation (sFCM) to design 1D material bodies with a specific dynamic eigenvalue spectrum is discussed. Such a formulated problem is based on the proper spatial distribution of material length scale, which maps the information about the underlying microstructure (it is important that the material length scale is one of two additional material parameters of sFCM compared to the classical local continuum mechanics—the second one, the order of fractional continua—is treated herein as a scaling parameter only). Technically, the design process for finding adequate length scale distribution is not trivial and requires the use of an inverse optimization procedure. In the analysis, the objective function considers a subset of eigenvalues reduced to a single value based on Kreisselmeier–Steinhauser formula. It is crucial that the total number of eigenvalues considered must be smaller than the limit which comes from the ratio of the sFCM length scale to the length of the material body.

Date of online publication

19.01.2020

Pages (from - to)

506-1 - 506-12

DOI

10.3390/en14020506

URL

https://www.mdpi.com/1996-1073/14/2/506

Comments

Article Number: 506

License type

CC BY (attribution alone)