Stability in an unbounded domain of a Timoshenko system without the second spectrum

The present paper deals with the stability, in the whole line ℝ, of the so-called truncated version for the Timoshenko system derived, according to significant physical and historical observations, by Elishakoff [11]. This new system gives a version of a Timoshenko-type beam model characterized by the absence of the second spectrum and its detrimental consequences for wave propagation speeds. Our objective is to prove the stability of this model, under certain conditions, using the energy method and Fourier analysis combined with some arguments devised in [16, 17, 18].