Diophantine type fractional derivative representation of structural hysteresis. I: Formulation. II: Fitting
type: Item
instance of: scholarly article
title: Diophantine type fractional derivative representation of structural hysteresis. I: Formulation. II: Fitting
zbMATH Open document ID: 0906.70013
published in: Computational Mechanics
publication date: 1999-02-16T00:00:00Z
review text: The hysteretic structural damping is more complex than traditional viscous structural damping. Under normal circumstances, the structural response can have such complications as frequency-dependent behavior, general multirate/history effects, and multi-phase time shifts. This paper develops a fractional derivative modeling scheme, based on diophantine representation of the operational powers, to simulate frequency-dependent structural damping. The diophantine set of powers together with a least square scheme are employed to construct a Chebyshev optimal integro-differential simulation of empirical data. This model fitting scheme enables the development of Kelvin-Voigt or Maxwell-Kelvin-Voigt fractional models for arbitrary experimental data. Due to the robustness of the scheme, any level of the representation accuracy is possible.
Mathematics Subject Classification ID: 70J35
Mathematics Subject Classification ID: 11D85
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 1084147
zbMATH Keywords: frequency-dependent behavior
zbMATH Keywords: operational powers
zbMATH Keywords: least square scheme
zbMATH Keywords: Chebyshev optimal integro-differential simulation
zbMATH Keywords: Maxwell-Kelvin-Voigt fractional models
zbMATH Keywords: experimental data
zbMATH Keywords: representation accuracy
author: Joe Padovan
author: Jerzy T. Sawicki
reviewed by: Yuri N. Sankin
MaRDI profile type: Publication
full work available at URL: s004660050182
OpenAlex ID: W1645564005
DOI: 10.1007/S004660050182
description: scientific article; zbMATH DE number 1084147