Cyclic Symmetric Structures Research Articles

Skyline solver for the static analysis of cyclic symmetric structures

A new solution technique is proposed for the static analysis of cyclic symmetric structures, in order to reduce computational effort. Efficient node numbering methods and the selection of a basic substructure for the cyclic symmetric analysis are suggested. Extension of cyclic symmetric analysis to an axisymmetric structure subjected to unsymmetric loading also is discussed. Another new method based on load norms is presented for selection of the Fourier harmonics indices for the analysis.

Lanczos method applied to the solution of eigenvalue problems of cyclic symmetric structures

The application of the Lanczos algorithm for the solution of eigenvalue problems connected with cyclic symmetric objects is studied. It is shown through a typical example that the approach remarkably reduces the computational effort without loss of accuracy.

Steady state stress analysis of centrifugal fan impellers

Cyclic symmetric structures such as centrifugal fan impellers are considered in this paper. One of the identical sectors is chosen for the finite element analysis. A triangular plate element is employed. The stiffness and load matrices are obtained in cylindrical coordinates. The displacements are obtained using a modified submatrices elimination scheme. The efficiency of this scheme is discussed. Impeller stresses are calculated and checked with the results obtained using a strain gauge technique.

An equation solver for eigenvalue problems of cyclic symmetric structures

To obtain the natural frequencies of rotationally periodic structures, a simple block solver is developed. Complex arithmetic is used to reduce the analysis region to a repeating substructure; characteristic matrices are considered to be cyclic in nature (S. Michimura et al., Bull. Jap. Soc. Mech. Engrs 24,1968–1993, 1981). Most of the decomposition operations involved in the complex stiffness matrix are done only once, also in real mode. Simple examples are included to illustrate this solution scheme. Triangular finite elements are used to form the characteristic matrices of repeating substructures.

Modes for deformable periodic cyclic symmetric systems driven in uniform rotation by a flexible shaft

An analysis is presented of the configurations which periodic cyclic symmetric structures can take when connected together in a repetitive pattern. One extremity is connected to a hub with a large, inherent, set rotation; this hub is then attached to a rotating flexible shaft. The modal analysis set out in this paper results in three uncoupled families of modes, each with its own gyroscopic coupling. The method is demonstrated on a relatively simple model.