Al-Jawi A., Mohamad A., Hawsawy A.

The dynamic behavior of a chain of cantilever beams, coupled by two rows of linear springs in a cyclic configuration is investigated. This simulates turbomachinery blades which are too long and have to be laced by two rows of stiffeners. A theoretical approach based on Green’s functions is used to obtain the exact solutions of the differentail equations of motion, which leads to the determination of the natural frequencies and mode shapes of the beams. The displacements of the constraint points in free vibration are calculated and used as a measure of mode localization. The finite element method (FEM, ABAQUS program) is also applied to the system, and the results are in excellent agreement with the theoretical. Using 12 beams and 24 springs of known mistuned properties, it is observed that for the doubly coupled cantilever beams, the first passband mode shapes (mode 1 upto mode 12) are weakly localized, but for the second and higher passbands, there is very strong localization. This is a new finding which should be of interest to turbomachinery designers.