Free Vibration Analysis of a Rotating Non-Uniform Blade with Multiple Open Cracks Using DQEM

Abstract In this paper, differential quadrature element method (DQEM) is used to analyze the free transverse vibration of a multiple cracked non-uniform Timoshenko blade rotating with a constant angular velocity. The blade’s deflection is assumed to be small so that the nonlinear terms can be neglected. Governing equations, compatibility conditions at the damaged cross-sections and boundary conditions are derived and formulated by the differential quadrature rules. First, the precision of the proposed method is confirmed by the exact solutions available in the literature. Then, the effect of angular velocity value as well as the location, depth and numbers of the cracks are investigated on the natural frequencies of the blade. The advantages of the proposed method are applicable for blades with any arbitrary variable section and less time-consuming for cases with several cracks