On the principle of cyclic symmetry in machine dynamics

Abstract

Cyclic symmetric structures are those that posses a circumferentially periodic geometry, e.g. gear wheels, bladed discs, etc. Accurate prediction of their static and dynamic characteristics is essential to ensure optimum design. An analysis of the entire structure is often prohibitively costly. Through illustrative examples, the essential features of an analysis scheme exploiting the geometric periodicity are brought out. Avoiding much of the mathematics, the underlying principle (termed the 'e^iψ relationship') for both static and dynamic analysis is explained. The parallel to the special case of axisymmetric structures is drawn.