In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a nite number of concentrated masses, elastic supports and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately deened Hilbert spa...

This study focuses on the problem of sound radiation by two concentric clamped flat plates, circular and annular, into the half-space. The system of three coupled differential equations comprising two equations of motions of plates and the wave equation, is solved exactly. Vibrations of plates are axisymmetric and time-harmonic with a single excitation frequency. The initial phase difference of...

Since shear waves in soft human tissues have been used clinics, little is known about their upper frequency behavior except that they fade out before the ultrasonic regime due to viscoelastic dissipation. Studying this bound has become a need micro-elastography aims at characterizing single cell using waves. We report through phantom experiments observation of 20.4 kHz. Moreover, it shown Kelvi...

Abstract The final value problem for the Brinkman–Forchheimer–Kelvin–Voigt equations is analysed quadratic and cubic types of Forchheimer nonlinearity. main term in allowed to be fully anisotropic. It shown that solution depends continuously on data provided satisfies an a priori bound $$L^3.$$ L <m...

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...

In this paper, we investigate the stabilization of a linear Bresse system with one discontinuous local internal viscoelastic damping Kelvin-Voigt type acting on axial force, under fully Dirichlet boundary conditions. First, using general criteria Arendt-Batty, prove strong stability our system. Finally, frequency domain approach combined multiplier method, that energy decays polynomially differ...

In this paper, the inverse problem for a linear system of Kelvin-Voigt equations with memory describing dynamics viscoelastic incompressible non-newtonian fluid is considered. under consideration, along solution (velocity and pressure) equation, it also required to find unknown (intensity external force) on right side, which depends only time variable. Definitions weak strong solutions are give...

We numerically model the human brain dynamics in realistic 2D cross-sections during traumatic scenarios corresponding to the Head Injury Criterion’s critical value HIC36=1000. Our simulations are based on the Kelvin-Voigt Partial Differential Equations that treat the brain tissue as a viscoelastic solid and on our nonlinear generalization of these linear PDEs that treats the tissue as an incomp...