Izvestiya of Saratov University.
Mathematics. Mechanics. Informatics
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

вязкоупругость

Waves in a viscoelastic cylindrical waveguide with a defect

In this paper, we consider a direct problem on waves in a viscoelastic inhomogeneous cylindrical waveguide with annular delamination and investigate an inverse problem on the identification of the delamination parameters on the basis of the additional data on the displacement field at the outer boundary of the waveguide. In order to account rheological properties within the framework of the complex modules concept, we use a model of a standard viscoelastic body.

Determination of Attaching Parameters of Inhomogeneous Beams in the Presence of Damping

Characterization of solids by additional data on displacements amplitudes or resonance frequencies have been increasingly attracting attention of researchers in recent years. Among the tasks of this type, the problems associated with definition of parameters describing boundary conditions and characterizing an interaction of the body studied with the surrounding bodies are of particular interest. In this paper, we investigate the problem of determining the parameters of the boundary conditions in a beam.

Development of Asymptotic Methods for the Analysis of Dispersion Relations for a Viscoelastic Solid Cylinder

Propagation of time-harmonic waves in a viscoelastic solid cylinder is considered. Vibrations of the cylinder are described by three-dimensional viscoelasticity equations in  cylindrical coordinates. The stress-free surface boundary conditions are imposed. Viscoelastic properties are described by integral operators with a fractional-exponential kernel. For the case of a rational singularity parameter the method of asymptotic analysis of dispersion relations is proposed, which is based on the generalized power series expansion.