Stability of a hybrid system with tip load damped

Abstract

In this article, we studied the stabilization of a hybrid system formed by a homogeneous and isotropic uniform bar clamped at the left end while the other is rigidly attached to a tip load damped. We prove that the C0-semigroup associated with this model has stability strong but not uniformly and decays polynomially at a rate of t−1/2. Finally, if we modify the homogeneity of a subpart of the end clamped of the bar through a thermoelastic inclusion, we achieve the uniform stability for the C0-semigroup associated with this new model. Such subpart is made of thermoelastic material different from its complementary but with an equal cross section.