A POWER-SERIES SOLUTION FOR VIBRATION OF A ROTATING TIMOSHENKO BEAM

Equations of motion for a rotating beam are developed based on the Timoshenko beam theory which includes the effects of rotary inertia and shear deformation. This leads to two variable-coefficient differential equations, for which only approximate solutions have been used in previous analyses. This paper presents a convergent power series expression to solve analytically for the exact natural frequencies and modal shapes of rotating Timoshenko beams. First, the results are presented for non-rotating Timoshenko beams and rotating Euler-Bernoulli beams and compared with existing solutions. Some errors existing in a previous result are pointed out and corrected. Then, the effects of rotary inertia and shear deformation on the dynamic characteristics of rotating beams are evaluated. The exact solutions can be used both as a direct analytical solution for practical engineering problems and as a bench mark for approximate numerical models.