This work presents a lossy partial differential acoustic wave equation including fractional derivative terms. It is derived from first principles of physics (mass and momentum conservation) and an equation of state given by the fractional Zener stress-strain constitutive relation. For a derivative order α in the fractional Zener relation, the resulting absorption α(k) obeys frequency power-laws...

The Viscoelastic response of hydropolymers, which include gelatin phantom and glandular breast tissue, may be accurately characterized with as few as three parameters using the Kelvin-Voigt Fractional Derivative (KVFD) modeling approach. We propose to image these parameters for simulated and experimental imaging phantoms and to estimate them for normal and cancerous in-vivo breast tissues. Afte...

In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions related to the Kelvin-Voigt damping and a delay term acting on the boundary. If the weight of the delay term in the feedback is less than the weight of the term without delay or if it is greater under an assumption between the damping factor, and the difference of the two weights, we prove the global ex...

Using low-stress pseudoshear deformation, we measured the ambient-temperaturecreep-recovery behavior of polycrystalline indium. The &+J diagram shows three regions with increasing stress: stress exponents of 1.05, 7.4, and 2.0. The diagram resembles remarkably the dislocation-velocity-shear-stressdiagrams reported for various materials by many authors, who interpreted the diagrams by dislocatio...

The generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermo-viscoelastic plane waves of assigned frequency in an infinite visco-elastic solid of Kelvin-Voigt type, when the entire medium rotates with a uniform angular velocity. A more general dispersion equation is deduced to determine the effects ...

The on-line or adaptive identification of parameters in abstract linear and nonlinear infinite-dimensional dynamical systems is considered. An estimator in the form of an infinitedimensional linear evolution system having the state and parameter estimates as its states is defined. Convergence of the state estimator is established via a Lyapunov estimate. The finite-dimensional notion of a plant...

The dynamic response of an initially flat viscoelastic membrane is investigated. The viscoelastic model is described with fractional order derivatives. The membrane is subjected to surface transverse and inplane dynamic loads. The governing equations are three coupled second order nonlinear partial FDEs (fractional differential equations) of hyperbolic type in terms of the displacement componen...

We numerically model the effects of repetitive human head motions in traumatic scenarios that are associated with severe brain injuries. Our results are based on the linear Kelvin-Voigt brain injury model, which treats the brain matter as a viscoelastic solid, and on our nonlinear generalization of that model, which emulates the gel-like character of the brain tissue. To properly compare the va...

Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actua-tors. Donnell-Mushtari equations, modiied to include Kelvin-Voigt damping, are used to model the system dynamics. Basis functio...

The Kelvin–Voigt model for a thin stratified two-dimensional visco-elastic strip is analyzed both in the quasistatic and dynamic cases. Neumann boundary conditions on upper lower parts of periodicity with respect to longitudinal variable are stated. A complete asymptotic expansion solution constructed cases, by using dimension reduction combined homogenization technique. error between exact one...