Free vibration of rotating cantilever pre-twisted panel with initial exponential function type geometric imperfection

•A new vibration mode for rotating blade with initial exponential function type geometric imperfection is provided.•The shallow shell theory is used and the mode involves the effect of the Coriolis and centrifugal force.•The effects of the geometries, imperfection and rotational speeds on the natural frequency is carried out.•It is very interesting to find that the internal resonance vibrations between modes due to imperfection.•The frequency veering phenomenon and mode shapes exchange between the modes are found due to imperfection. The machining errors and the geometric imperfections are unavoidable, such as, local indentations, surface form error, flat curve form error and non-uniform thickness and so on. In this paper, a new vibration model for the rotating blade which is treated as a cantilever pre-twisted panel with initial exponential function type geometric imperfection is provided by using the shallow shell theory in which the torsion is considered but the two radii of curvatures are zero. Also, this mode involves the effect of the Coriolis and centrifugal force. It is assumed that the material of the pre-twisted curved panel is homogeneous and isotropic. Based on the Rayleigh–Ritz method and continuous algebraic polynomial functions satisfying the cantilever boundary conditions, the natural frequencies and mode shapes of perfect rotating pre-twisted curved panel and those with the initial geometric imperfection are computed. The validity of this model is verified by comparison with ANSYS results. A comprehensive study about the effects of the geometric parameters, imperfection size, imperfection location and the concentration degree of it, pre-twisted angles, setting angle and rotational speeds of the pre-twisted curved panel on the free vibration is carried out. The problems of frequency veering, mode shape shift, internal resonance between modes and effect of dynamic stiffness can be found.