On initial conditions for a boundary stabilized hybrid Euler-Bernoulli beam

We consider here small flexural vibrations of an Euler-Bernoulli beam with a Jumped mass at one end subject to viscous damping force while the other end is free and the system is set to motion with initial displacement y(o)(x) and initial velocity y(1)(x). By investigating the evolution of the motion by Laplace transform, it is proved (in dimensionless units of length and time.) that integral (1)(0) y(xt)(2) dx less than or equal to integral (1)(0) y(xx)(2) dx, t > t(0), where t(0) may be sufficiently large, provided that {y(0), y(1)} satisfy very general restrictions stated in the concluding theorem. This supplies the restrictions for uniform exponential energy decay for stabilization of the beam considered in a recent paper.