Parametric studies on bending vibration of axially-loaded twisted Timoshenko beams with locally distributed Kelvin–Voigt damping

• Increasing twist angle decreases decay rate of mode 1 but increases that of mode 2.
• The damped segment size, location and damping greatly affect the eigenfrequencies.
• Effects of damping value on eigenfrequencies vary depending on restraint types.
• Increasing axial load always decreases the damped oscillation frequencies.
• Increasing axial load may increase or reduce the decay rate of free vibration.

Using the Timoshenko beam theory and applying Hamilton׳s principle, the present study establishes bending–bending vibrations of an axially loaded twisted beam with locally distributed Kelvin–Voigt damping. 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 equations of motion into linear second-order ordinary differential equations with constant coefficients. A quadratic eigenvalue problem of a damped system is formulated to study the effects of the twist angle, damping amount, size and location of damped segment, axial load and restraint types on the eigenfrequency of the damped twisted beams. It is believed that the present model is valuable for the parametric studies to understand better the various variables of the damped twisted beam affecting its vibration characteristics.