Damped vibration of a non-prismatic beam with a rotational spring

In this paper a problem pertaining to the damped lateral vibrations of a beam with different boundary conditions and with a rotational spring is formulated and solved. In the adopted model the vibration energy dissipation derives from the internal damping of the viscoelastic material (Kelvin–Voigt rheological model) of the beam and from the resistance motion in the supports. The rotational spring can be mounted at any chosen position along the beam length. The influence of step changes in the cross-section of the beam on its damped lateral vibrations is also investigated in the paper. The damped vibration frequency and the vibration amplitude decay level are calculated. Changes in the eigenvalues of the beam vibrations along with the changes in the damping ratio and the change in the model geometry observed on it are also presented. The considered beam was treated as Euler- Bernoulli beam.