Fractional Rheological Constitutive Equations
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration shows the simplest two-element fractional rheological constitutive models. Choose between the constitutive model, the type of rheological experiment, and the plot type. Use the sliders to vary the fractional power-law exponents of the two springpots independently (
and 
), and their corresponding quasi-properties (
and 
). The convention for the exponents used here is 
.
Contributed by: Aditya Jaishankar (October 2013)
Open content licensed under CC BY-NC-SA
Snapshots
Details
More details about fractional constitutive equations and power-law rheology can be found in the references.
References
[1] A. Jaishankar and G. H. McKinley, "Power-Law Rheology in the Bulk and at the Interface: Quasi-Properties and Fractional Constitutive Equations," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469(2149), 2013. doi.10.1098/rspa.2012.0284.
[2] C. Friedrich, "Relaxation and Retardation Functions of the Maxwell Model with Fractional Derivatives," Rheologica Acta, 30(2), 1991 pp. 151–158. www.springerlink.com/index/j3523m37x311557l.pdf.
[3] H. Schiessel, R. Metzler, A. Blumen, and T. Nonnenmacher, "Generalized Viscoelastic Models: Their Fractional Equations with Solutions," Journal of Physics A: Mathematical and General, 28(23), 1995 pp. 6567–6584. iopscience.iop.org/0305-4470/28/23/012.
[4] I. Podlubny, Fractional Differential Equations (Mathematics in Science and Engineering, Vol. 198), San Diego: Academic Press, 1999.
Permanent Citation
Improving Power Factors in an AC Circuit
Anping Zeng
Simulating the Power Factor of an AC System
Harley H. Hartman
AC Synchronous Machine Vector Diagram
Harley H. Hartman
AC Three-Phase Neutral Current
Harley H. Hartman
AC Power Factor Principle
Harley H. Hartman
AC Thyristor Trigger Angle versus Power Factor
Harley H. Hartman
Operating an AC Three-Phase Induction Motor
Harley H. Hartman
Simulating the Neutral Current of an AC System
Harley H. Hartman
Pulse Width Modulation Principle
Harley H. Hartman
AC Thyristor Operation
Harley H. Hartman
