Second and Higher Order Harmonic Finite Elements for the Study of the Dynamics of Bladed Discs

Annular finite elements for the computation of second and higher order harmonics modes of bladed rotating discs are developed. The elements take into account gyroscopic effect and stiffening due to centrifugal and thermal stresses (the latter not present in arrays of blades). The displacement field is expressed by a truncated Fourier series along the angle and by polynomial shape functions in the radial direction. This paper is the generalization of previous study limited to zero and first order harmonics and deals only with higher order harmonics modes that are uncoupled from the modes involving the behavior of the rotor as a whole. Several cases have been studied to verify the accuracy of the disc and array of blades elements.