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

摘要

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 AN-SYS 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. (C) 2018 Elsevier Inc. All rights reserved.