Shahriar Hosseini Hashemi - BSc. Student School of Mechanical and Aerospace Engineering, Islamic Azad University, Science and Research Branch
Adel Magsud Pour - Assistant professor School of Mechanical and Aerospace Engineering, Islamic Azad University, Science and Research Branch
Alireza Nezamabadi - Assistant Professor School of Mechanical Engineering, Islamic Azad University, Arak Branch

The exact closed form characteristic equations are given within the validity of the Timoshenko beam theoryfor beams having classical boundary conditions. Accurate eigenvalue parameters are presented for different heightto length ratio. The modal tests are performed for beams with clamped-Free and Free-Free boundary conditions.Validity of the derived closed form characteristic equations are examined through comparison of numerical solutionswith the experimental work and available data in the literature. It is believed that in the present work, the exactclosed form characteristic equations for most of considered cases are obtained for the first time.

Bench mark equation, Transverse vibration, Timoshenko beam, Characteristic equation