Exponential decay of serially connected elastic wave

Abstract

In this work we study a flexible structures which is formed by three serially connected elastic waves, more specifically on structure whose material consist of three different types of components where one is purely elastic component and two dissipative elastic. We show that for this types of materials the dissipation produced by the dissipative elastic part is strong enough to produce exponential decay of the solution, no matter how small is its size. We also show that the linear model is well posed.