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

Energies

Tomasz Blaszczyk¹  Krzysztof Bekus¹  Krzysztof Szajek²  Wojciech Sumelka² 

[1] Department of Mathematics, Czestochowa University of Technology, 42-201 Częstochowa, Poland;Institute of Structural Analysis, Poznan University of Technology, 60-965 Poznań, Poland;

关键词: discrete model;    continuum non-local model;    fractional calculus;    fractional mechanics;   

DOI  :  10.3390/en14020506

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown