Green's functions of the forced vibration of Timoshenko beams with damping effect

• The dynamic Green's function of a Timoshenko beam with damping effects is obtained.
• The present work is performed in a systematic manner.
• The validity of the present solutions is checked in analytical and numerical ways.
• The effects of various parameters are examined numerically.

This paper is concerned with the dynamic solutions for forced vibrations of Timoshenko beams in a systematical manner. Damping effects on the vibrations of the beam are taken into consideration by introducing two characteristic parameters. Laplace transform method is applied in the present study and corresponding Green's functions are presented explicitly for beams with various boundaries. The present solutions can be readily reduced to those for others classical beam models by setting corresponding parameters to zero or infinite. Numerical calculations are performed to validate the present solutions and the effects of various important physical parameters are investigated.