Natural frequencies of the elastically end restrained non-uniform Timoshenko beam using the power series method

Abstract

In recent years, the transverse vibration of the uniform Timoshenko beam has become a highly significant research topic. The Timoshenko beam (TB) model is suitable for describing the behavior of the beams under high-frequency excitation load when the wavelength approaches the thickness of the beam because it considers the shear deformation and the rotational inertia effects. In this paper, the natural frequencies of the elastically end constrained nonuniform TB is discussed. For this reason, the nonuniform TB is modeled by an exact and direct modeling technique. The semi-analytical solution based on the power series method is adopted in technique. The effect of the spring supports, different boundary conditions, the non-uniformity in the cross-section of the TB, and other parameters are assessed. The results are shown that the nonuniformity in the cross-section of the beam is impressed on the natural frequencies. On the other hand, the presented formulation not only effectively is easy to use, but also provides the reasonable solution of non-uniform TB, carrying various boundary conditions.

Keywords:

• Nonuniform Timoshenko beam
• free vibration
• general boundary conditions
• power series method