Free vibration analysis of cyclic symmetric structures by finite element and boundary element methods

Te current numerical methods used to determine dynamic behavior of cyclic symmetric structure under rotational operating conditions remain somewhat limited. Certain issues relating to centrifugal stiffening have not been adequately addressed. One of the objectives of this dissertation is directed towards the development of methodologies and numerical techniques needed to accurately and efficiently predict the dynamic characteristics of spinning cyclically symmetric structures. A detailed investigation into finite element method (FEM) formulations for eigenvalue analysis of periodically rotational structures is conducted. Included is an examination of centrifugal stiffening effects and the development of relevant correlation approaches. This work also develops a general modal cyclic symmetry analysis approach within the boundary element method (BEM). Advanced FEM and BEM implementations are then applied in two case studies of a circular disk and a turbine impeller. These case studies are intended to provide an objective assessment of the alternative methodologies. Correlation studies are also conducted using experimental data to validate the approaches. As a further improvement, research effort is directed toward the development of new algorithms that utilize wavelets within the context of BEM. The investigation of several one-dimensional model problems indicates that this approach has significant potential. With continued development, these wavelet-based algorithms may ultimately extend the application scope of BEM to very large-scale engineering problems.