Free vibration of a Timoshenko beam carrying three dimensional tip mass: Analytical solution and experimental modal testing

Abstract

In this work, free vibration of a Timoshenko beam carrying three dimensional tip mass whose center of gravity is not coincident with beam end is dealt with. The beam performs bending in two orthogonal planes plus torsional deformation about the beam axis. Since the tip mass center of gravity is not coincident with beam end point, these deformations are coupled through the boundary conditions. First, an analytical model is developed for the considered system and solved. Later, the analytical results are compared with the experimental and finite element results. Experimental values are obtained by the impact testing, and peak picking approach is employed to extract modal data. Furthermore, finite element results are obtained by ANSYS, a famous finite element software. According to the relevant literature, this is the first study including experimental data for the considered system. It is observed that analytical results, in general, agree with the numerical and experimental results. Thus, the analytical model developed in this work may safely be used for later studies where lower modal data of the structure is required.