Diophantine type fractional derivative representation of structural hysteresis. I: Formulation. II: Fitting
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.
Chebyshev optimal integro-differential simulation
scientific article; zbMATH DE number 1084147