Existence of solution and uniform decay for a contact problem in laminated beam.

• For existence of weak solution in Signorini's contact problem in the previous works was used the Div-Curl lemma. • We follow a different and new approach applying the semigroup theory. • We prove the existence of at least one solution to the Signorini problem by using the hybrid-penalized method. • We prove uniform stabilization assuming equal wave speeds in the first and second equations of the system. • The uniqueness of the solution to Signorini's problem remains an open question. In this paper, we study Signorini's problem for a laminated Timoshenko beam with interfacial slip. We assume that the transverse displacements at the end of the beam are in the presence of two rigid obstacles (Signorini conditions). We prove the existence of solution and analyze the asymptotic behavior of the system. We use the hybrid-penalized method to show the global existence of at least one solution to Signorini's problem and finally, numerical experiments verify the theoretical results. [ABSTRACT FROM AUTHOR]