We consider the hybrid laminated Timoshenko beam model. This structure is given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. We suppose that the beam is fastened securely on the left while on the right it's free and has an attached container. Using the semigroup approach and a result of Borichev and Tomilov, we prove that the solution is polynomially stable. Published by AIP Publishing.