Stabilization of Quasi-Linear Vibrations of an Inhomogeneous Beam

In this note, we study the stabilization of a vibrating inhomogeneous beam under distributed disturbing force. We prove that the amplitude of such vibration is bounded subject to some restriction on the uncertain disturbing force. We also estimate the total energy of the system over time interval [0,T] for any time T > 0 , together with a tolerance level of the disturbance. Finally, we establish the uniform decay of solution with an explicit form of exponential energy decay estimate, when the uncertain disturbances are insignificant.