arXiv subjects

Malgorzata Seredynska

Publications and source records attributed to Malgorzata Seredynska.

3 recordsLinked to original sources

arXiv2011

Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy

Spatial non-locality of space-fractional viscoelastic equations of motion is studied. Relaxation effects are accounted for by replacing second-order time derivatives by lower-order fractional derivatives and their generalizations. It is shown that space-fractional equations of motion of an order strictly less than 2 allow for a new kind anisotropy, associated with angular dependence of non-local interactions between stress and strain at different material points. Constitutive equations of such viscoelastic media are determined. Explicit fundamental solutions of the Cauchy problem are constructed for some cases isotropic and anisotropic non-locality.

math-ph↗

arXiv2010

Attenuation, dispersion and finite propagation speed in viscoelastic media

It is shown that the dispersion and attenuation functions in a linear viscoelastic medium with a positive relaxation spectrum have a sublinear growth rate at very high frequencies. A local dispersion relation in parametric form is found. The exact limit between attenuation growth rates compatible and incompatible with finite propagation speed is found. Incompatibility of superlinear frequency dependence of attenuation with finite speed of propagation and with the assumption of positive relaxation spectrum is demonstrated.

math-ph↗

arXiv2009

Positive solutions of viscoelastic problems

In 1,2 or 3 dimensions a scalar wave excited by a non-negative source in a viscoelastic medium with a non-negative relaxation spectrum or a Newtonian response or both combined inherits the sign of the source. The key assumption is a constitutive relation which involves the sum of a Newtonian viscosity term and a memory term with a completely monotone relaxation kernel. In higher-dimensional spaces this result holds for sufficiently regular sources. Two positivity results for vector-valued wave fields including isotropic viscoelasticity are also obtained. Positivity is also shown to hold under weakened hypotheses.

cond-mat.mtrl-sci↗