A new dynamic model for a rotating beam carrying extra partially distributed mass

In this paper, a new dynamic model for the vibration analysis of an inward-oriented rotating cantilever beam with extra distributed mass was presented. The derived differential equation of motion was solved using the meshless methods of generalized Multiquadric Radial Basis Function (RBF) and the eigenfrequencies of the system were determined. The same problem was also modeled using the finite element method and the results were compared to validate the accuracy of the proposed model. Later, the effect of the partially distributed mass amount and location on the eigenfrequencies was studied for various beam lengths. The results showed that the eigenfrequency at a constant rotational speed mostly decreased unless the mass was located at the free end of the beam. The location of the mass had a greater effect on the first eigenfrequency compared to the second and third eigenfrequencies. A joint dimensionless eigenfrequency was found at a specific rotational speed regardless of the distributed mass. Nearly constant dimensionless eigenfrequencies could be obtained for a wide range of rotational speeds by adjusting the distributed mass.