Three-dimensional vibration analysis of rotating pre-twisted variable thickness blades composed of spanwise graded functional materials

In this study, the isogeometric method is used to obtain a three-dimensional (3-D) solution for the vibration of rotating pre-twisted blades composed of spanwise functionally graded materials (SFGM). The material properties are assumed to change continuously in the spanwise direction according to a mixture rule. Nonuniform rational B–splines (NURBS) are used to describe the unknown displacement and geometry of the rotating blades, whose thickness linearly tapers along the spanwise direction. A typical isogeometric element for a rotating pre-twisted variable thickness SFGM blade is introduced to prevent transformations among multiple coordinate systems. This model considers centrifugal stiffening, centrifugal softening, and Coriolis force effects. Several cases are studied, including rotating rectangular plates, partial cylindrical shells and conical shells with different material properties and geometric parameters. The predicted vibration behaviors are verified by comparisons with results from the literature and commercial finite element software. The comparisons show that the current model has good accuracy. Finally, the influence of material properties, rotating speeds, installation angles, pre-twist angles, and variable thicknesses on the vibrational characteristics of rotating pre-twisted SFGM blades are examined.