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    Free vibration of a Timoshenko beam carrying three dimensional tip mass: Analytical solution and experimental modal testing
    (Carl Hanser Verlag, 2017) Katı Doğanay, Hilal; Gokdag, Hakan
    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.
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    Vibration analysis of a Timoshenko beam carrying 3D tip mass by using differential transform method
    (Techno-Press, 2018) Katı Doğanay, Hilal; Gokdag, Hakan
    Dynamic behaviour of beam carrying masses has attracted attention of many researchers and engineers. Many studies on the analytical solution of beam with concentric tip mass have been published. However, there are limited works on vibration analysis of beam with an eccentric three dimensional object. In this case, bending and torsional deformations of beam are coupled due to the boundary conditions. Analytical solution of equations of motion of the system is complicated and lengthy. Therefore, in this study, Differential Transform Method (DTM) is applied to solve the relevant equations. First, the Timoshenko beam with 3D tip attachment whose centre of gravity is not coincident with beam end point is considered. The beam is assumed to undergo bending in two orthogonal planes and torsional deformation about beam axis. Using Hamilton's principle the equations of motion of the system along with the possible boundary conditions are derived. Later DTM is applied to obtain natural frequencies and mode shapes of the system. According to the relevant literature DTM has not been applied to such a system so far. Moreover, the problem is modelled by Ansys, the well-known finite element method, and impact test is applied to extract experimental modal data. Comparing DTM results with finite element and experimental results it is concluded that the proposed approach produces accurate results.