Free vibration of an extensible rotating inclined Timoshenko beam

An exact power-series solution for free vibration of a rotating inclined Timoshenko beam is developed. It is shown that both the extensional deformation and the Coriolis force will have significant influence on the natural frequencies of the rotating beam when the dimensionless rotating extension parameter is large. Without numerical analysis, several general qualitative relations among the inclination angle, the hub radius and the natural frequencies of the beam are revealed. In addition, the influence of extensional deformation in the centrifugal stiffening force term on the natural frequencies evaluated by the Timoshenko and the Euler beam theories is also studied and compared.