Abstract. In this paper we consider the transmission problem of a material composed of three components; one of them is a Kelvin–Voigt viscoelastic material, the second is an elastic material (no dissipation), and the third is an elastic material inserted with a frictional damping mechanism. The main result of this paper is that the rate of decay will depend on the position of each component. W...

The object of considerations is a thin linear-elastic cylindrical shell having a periodic structure (i.e. a periodically varying thickness and/or periodically varying elastic and inertial properties) in both directions tangent to the shell midsurface. Such shells are called biperiodic. The aim of this paper is to propose a new averaged non-asymptotic model of biperiodic shells, which makes it p...

We analyze the consistency, stability, and convergence of an hp discontinuous Galerkin spectral element method. The analysis is carried out simultaneously for acoustic, elastic, coupled elastic–acoustic, and electromagnetic wave propagation. Our analytical results are developed for both conforming and non-conforming approximations on hexahedral meshes using either exact integration with Legendr...