Vibration analysis of a beam with partially distributed internal viscous damping

In this paper, governing equations of vibration for a beam with distributed internal viscous damping are established by using Timoshenko beam theory and Hamilton's principle. Then, the transfer matrix method is applied to obtain the frequency equations for the beam. The results reveal, when the internal viscous damping fully distributes along the beam, that the natural frequency decreases with the increasing damping and drops to a zero value at a certain critical damping. While the damping is locally distributed, damped frequency, mode shape and transient response time are affected most significantly by locating the damped segment at the position with maximum bending moment. The flexural amplitudes and phase angles of a beam excited by the resonant harmonic load can be effectively predominated by tuning the damping value.