Nonlinear dynamic analysis on centrifugal stiffening of rotating cracked tapered functionally graded beam for flap-wise vibrations

Vibration-based condition monitoring for remotely located rotating blades is one of the important aspects to avoid sudden breakdown of the machinery. Vibration analysis of damaged blades provides the information to identify the damage during operation. In this work, dynamic attributes of rotating cracked tapered cantilever functionally graded material (FGM) beams for various tapered configurations are investigated using energy method. The nonlinearity due to in plane stretching as a result of large deformations is taken in to consideration. Nonlinear governing equations for cracked rotating tapered FGM beams are generated by optimizing the energy functional. An iterative algorithm is developed to solve the derived nonlinear equations. The effects corresponding to location of crack and centrifugal stiffening on the various modes has been presented for different tapered configurations, material indices, crack depths and rotational speeds. Crack compensating speeds are studied and reported for different tapered ratios and crack parameters for the first time. The effect of crack location and crack depth on the first two nonlinear frequency ratios is also investigated for different tapered configurations and material indices. The influence of centrifugal stiffening on nonlinear responses of FGM beams is presented for various crack parameters and tapered configurations.