Simplified modelling and analysis of a rotating Euler-Bernoulli beam with a single cracked edge. (28th April 2018) - Yashar, Ahmed; Ferguson, Neil; Ghandchi-Tehrani, Maryam
Abstract: The natural frequencies and mode shapes of the flapwise and chordwise vibrations of a rotating cracked Euler-Bernoulli beam are investigated using a simplified method. This approach is based on obtaining the lateral deflection of the cracked rotating beam by subtracting the potential energy of a rotating massless spring, which represents the crack, from the total potential energy of the intact rotating beam. With this new method, it is assumed that the admissible function which satisfies the geometric boundary conditions of an intact beam is valid even in the presence of a crack. Furthermore, the centrifugal stiffness due to rotation is considered as an additional stiffness, which is obtained from the rotational speed and the geometry of the beam. Finally, the Rayleigh-Ritz method is utilised to solve the eigenvalue problem. The validity of the results is confirmed at different rotational speeds, crack depth and location by comparison with solid and beam finite element model simulations. Furthermore, the mode shapes are compared with those obtained from finite element models using a Modal Assurance Criterion (MAC). Highlights: A novel prediction model for vibration of a rotating cracked beam is presented. The effects of crack location and depth on the natural frequencies and modes are shown. Veering in the chordwise plane modes for a cracked rotating beam are illustrated.