Boundary Stabilization of the Rao-Nakra Beam And Dual-Phase-Lag One-Dimensional Thermo-Porous-Elasticity with Microtemperatures

Abstract

The Rao-Narka beam is a laminated 3-layer beam with the top and bottom layers being made up of a linear elastic material. The core is made up of a material such that the shear stress is related to the shear strain. Recent papers have been able to achieve exponential or polynomial stability with a specific configuration of the feedback controllers. We examine a new case where the top and bottom layers are the only layers with this boundary damping. Using the frequency domain approach we are able to show that the system is polynomially stable of order 1/3 when the wave speed is the same. Before we show this, we construct a proper state space so the system is dissipative. Then, we will show the first-order evolution equation is a infinitesimal generator of a C_0-Semigroup of contraction using semigroup theory.