Frequency Veering of Rotating Metal Porous Twisted Plate with Cantilever Boundary Using Shell Theory

The frequency veering of a metal porous rotating cantilever twisted plate with twist angle and stagger angle is investigated. Metal porous materials may have the characteristics of gradient or uniform distribution along the thickness direction. Based on the classical shell theory, considering the influence of centrifugal force produced by high-speed rotation, the free vibration equations of a rotating cantilever twisted plate are derived. Through the polynomial function and Rayleigh–Ritz method, the natural frequencies and mode shapes of the metal porous cantilever twisted plate in both static and rotating states are derived. The accuracy of the present theory and calculation results is confirmed by a comparison between them and the results available from the literature and those obtained from Abaqus. The influences of the thickness ratio, porosity, twist angle, stagger angle and rotational velocity on the frequency veering and mode shape shift of the rotating cantilever twisted plate with porous material under three different distributions are analyzed. It should be mentioned that the frequency veering accompanied by mode shape shift occurs in both static and dynamic states.