105 citations · 173 across the 19 of their papers we have counts for
20 papers
On solutions of matrix-valued convolution equations, anisotropic fractional derivatives and their applications in linear and non-linear anisotropic viscoelasticity
Andrzej Hanyga
A relation between matrix-valued complete Bernstein functions and matrix-valued Stieltjes functions is applied to prove that the solutions of matricial convolution equations with e…
A comment on a controversial issue: a Generalized Fractional Derivative cannot have a regular kernel
Andrzej Hanyga
The problem whether a given pair of functions can be used as the kernels of a generalized fractional derivative and the associated generalized fractional integral is reduced to the…
Effects of Newtonian viscosity and relaxation on linear viscoelastic wave propagation
Andrzej Hanyga
In an important class of linear viscoelastic media the stress is the superposition of a Newtonian term and a stress relaxation term. It is assumed that the creep compliance is a Be…
On solutions of a class of matrix-valued convolution equations
Andrzej Hanyga
We apply a relation between matrix-valued complete Bernstein functions and matrix-valued Stieltjes functions to prove that certain convolution equations for matrix-valued functions…
A simple proof of a duality theorem with applications in scalar and anisotropic viscoelasticity
Andrzej Hanyga
A new concise proof is given of a duality theorem connecting completely monotone relaxation functions with Bernstein class creep functions in one-dimensional and anisotropic 3D vis…
A simple proof of a duality theorem with applications in viscoelasticity
Andrzej Hanyga
A new concise proof is given of a duality theorem connecting completely monotone relaxation functions with Bernstein class creep functions. The proof makes use of the theory of com…
Plane waves in anisotropic viscoelastic media
Andrzej Hanyga
Two concepts of plane waves in anisotropic viscoelastic media are studied. One of these concepts allows for the use of methods based on the theory of complete Bernstein functions.…
Elimination of memory from the equations of motion of hereditary viscoelasticity for increased efficiency of numerical integration
Andrzej Hanyga
A method of eliminating the memory from the equations of motion of linear viscoelasticity is presented. Replacing the unbounded memory by a quadrature over a finite or semi-finite…
Wave propagation in anisotropic viscoelasticity
Andrzej Hanyga
We extend the theory of complete Bernstein functions to matrix-valued functions and apply it to analyze Green's function of an anisotropic multi-dimension\-al linear viscoelastic p…
Attenuation and shock waves in linear hereditary viscoelastic media. Strick-Mainardi, Jeffreys-Lomnitz-Strick and Andrade creep compliances
Andrzej Hanyga
Dispersion, attenuation and wavefronts in a class of linear viscoelastic media proposed by Strick and Mainardi in 1982 and a related class of models due to Lomnitz, Jeffreys and St…
Asymptotic estimates of viscoelastic Green's functions near the wavefront
Andrzej Hanyga
Asymptotic behavior of viscoelastic Green's functions near the wavefront is expressed in terms of a causal function defined in \cite{SerHanJMP} in connection with the Kramer…
An acoustic wave equation based on viscoelasticity
Andrzej Hanyga
An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It is assumed that the relaxation moduli are comple…
Dispersion and attenuation for an acoustic wave equation consistent with viscoelasticity
Andrzej Hanyga
An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It differs significantly from the equations propose…
On wave propagation in viscoelastic media with concave creep compliance
Andrzej Hanyga
It is proved that the attenuation function of a viscoelastic medium with a non-decreasing and concave creep compliance is sublinear in the high frequency range.
Wave propagation in linear viscoelastic media with completely monotonic relaxation moduli
Andrzej Hanyga
It is shown that viscoelastic wave dispersion and attenuation in a viscoelastic medium with a completely monotonic relaxation modulus is completely characterized by the phase speed…
Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy
Andrzej Hanyga, Malgorzata Seredynska
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…
Theory of attenuation and finite propagation speed in viscoelastic media
M. Seredyńska, Andrzej Hanyga
It is shown that the dispersion and attenuation functions in a linear viscoelastic medium with a positive relaxation spectrum can be expressed in terms of a positive measure. Both…
Attenuation, dispersion and finite propagation speed in viscoelastic media
Malgorzata Seredynska, Andrzej Hanyga
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.…
Positive solutions of viscoelastic problems
Malgorzata Seredynska, Andrzej Hanyga
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 inhe…
Cones of material response functions in 1D and anisotropic linear viscoelasticity
M. Seredyńska, A. Hanyga
Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. It is s…