Response of rotating rings to harmonic and periodic loading and comparison with the inverted problem
The harmonic and periodic forced vibrations of rotating rings are derived and investigated. The modal expansion technique yields the forced solution, which is characterized by four generalized co-ordinates associated with each n (circumferential wave number). The inextensional assumption is presumed, when flexural vibration is the only important component, to reduce the order of the system. The closed form solutions to the harmonic load cases, once concentrated, once distributed, are demonstrated and interpreted. The approach is then extended to periodic loads, where Fourier sine and cosine series is applied. Examples depict the numerical responses to all the cases being derived. The solutions of a stationary ring subjected to traveling loads are also solved for comparison. Their difference is investigated and interpreted from various viewpoints.