Bending vibration of axially loaded Timoshenko beams with locally distributed Kelvin–Voigt damping

Utilizing the Timoshenko beam theory and applying Hamiltonʹs principle, the bending vibration equations of an axially loaded beam with locally distributed internal damping of the Kelvin–Voigt type are established. The partial differential equations of motion are then discretized into linear second-order ordinary differential equations based on a finite element method. A quadratic eigenvalue problem of a damped system is formed to determine the eigenfrequencies of the damped beams. The effects of the internal damping, sizes and locations of damped segment, axial load and restraint types on the damping and oscillating parts of the damped natural frequency are investigated. It is believed that the present study is valuable for better understanding the influence of various parameters of the damped beam on its vibration characteristics.