Vibration Analysis of Twisted Timoshenko Beams with Internal Kelvin-Voigt Damping

Bending-bending vibration equations of a twisted beam with damping of Kelvin-Voigt type are established using the Timoshenko beam theory and applying Hamilton's principle. The equations of motion of the twisted beam are derived in the twist coordinate frame. Then, a finite element method is used to reduce the partial differential equations of motion into linear second-order ordinary differential equations. A quadratic eigenvalue problem of a damped system is formulated to study the effects of the twist angle, internal damping and restraint types on the eigenfrequencies of the damped twisted beams.