Non-linear vibration of rotating cantilever blades treated by the Ritz averaging process

Abstract

The prediction of the forced vibration response of rotating cantilever blading is of considerable importance in the design of turbine and compressor blading where the rotational speeds are relatively high. Non-linearities in the blades arise from the effects of Coriolis accelerations due to the rotation of the blades mounted on the periphery of the disc.Lo and Renbarger derived the differential equations of motion of a cantilever beam mounted on a rotating disc at a given stagger angle and show, for a linear case, that the frequencies of a bar vibrating transversely to a plane inclined at an angle to the plane of rotation can be found by a simple transformation of the frequencies of vibration perpendicular to the plane of rotation. Boyce, Di Prima and Handelman applied the Rayleigh-Ritz and Southwell methods to the case of a turbine blade vibrating perpendicular to the plane of rotation and determined the upper and lower bounds of the natural frequencies.