Kocatürk T., Simsek M., Ýlhan N.

Passive techniques in vibration damping is of considerable interest to engineers designing structural and mechanical systems such as chimneys of plants, communication towers, manipulator arms and many others. As is known, vibration damping is very important in engineering practice. In some cases, the damping treatments at boundaries can be an alternative solution to surface damping treatments with viscoelastic materials for beams and plates. In this study, steady-state response with respect to base movement of a viscoelastically supported viscoelastic cantilever beam with a tip mass is analyzed by using the principle of relative motion within the framework of the Euler-bernoulli beam theory. Kelvin-Voigt model is used for the material of the beam. The Lagrange equations are used to examine the dynamic behaviour of a viscoelastically supported cantilever beam with the tip mass under sinusoidally varying base excitation. The constraint condition against rotation of the supported end is taken into account by using the Lagrange multipliers. In the study, for applying the Lagrange equations, the trial functions denoting deflection of the beam is expressed in polynomial form. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The influence of the support damping and internal damping on the steady-state response of the beam with the tip mass is investigated numerically for various external and internal damping parameters, support stiffness parameter and mass ratio (the ratio of the mass to the tip mass to the mass of the beam). The results are obtained within the forced frequency range which contains the first two natural frequencies of the cantilever beam.