Fractional-order Spectra for Complex Viscoelastic Materials
نویسندگان
چکیده
Recently much of the research has been dedicated to the application of fractional calculus in rheology. In this paper fractional-order spectra are presented for the complex viscoelastic materials, which mechanical analogy are constructed by fractional elements connected in series or parallel. Fractional-order spectra connect directly to the material’s constitutive relation with fractional derivatives and reflect the characteristic of networks of mechanical analogy. The calculation method for fractional-order spectra is provided. The spectra for some fractional models which are commonly used are determined.
منابع مشابه
Thermo-Viscoelastic Interaction Subjected to Fractional Fourier law with Three-Phase-Lag Effects
In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts the...
متن کاملVibration of FG viscoelastic nanobeams due to a periodic heat flux via fractional derivative model
In this work, the vibrations of viscoelastic functionally graded Euler–Bernoulli nanostructure beams are investigated using the fractional-order calculus. It is assumed that the functionally graded nanobeam (FGN) is due to a periodic heat flux. FGN can be considered as nonhomogenous composite structures; with continuous structural changes along the thick- ness of the nanobeam usually, it change...
متن کاملA Fractional K-BKZ Constitutive Formulation for Describing the Nonlinear Rheology of Multiscale Complex Fluids
The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law–like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally...
متن کاملA fractional-order model on new experiments of linear viscoelastic creep of Hami Melon
This paper describes our experimental testing of linear viscoelastic creep behaviours in HamiMelon. Experimental data shows that HamiMelon has complex viscoelastic property which cannot be well described by the standard model. Consequently, this study develops a fractional derivative model to describe such complex viscoelastic creep behaviours of Hami Melon. The analytical creep function of the...
متن کاملFractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms
We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compar...
متن کامل