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. © 1990.

D. G. Mangsuli

Viswanatha Ramamurti

MATHEMATICAL TECHNIQUES - Eigenvalues and Eigenfunctions

Vibrations - Analysis

CYCLIC SYMMETRIC STRUCTURES

LANCZOS ALGORITHM

Structural analysis

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IIT Madras

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

Computers and 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. Engrs24,1968-1993, 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. © 1987.

An equation solver for eigenvalue problems of cyclic symmetric structures

In-plane analysis of annular disks using the finite element method is presented. A semi-analytical, one-dimensional finite element model is developed using a Fourier series approach to account for the circumferential behaviour. Using displacement functions which are exact solutions of the two dimensional elasticity plane stress problem, the shape functions, stiffness matrices and mass matrices corresponding to the 0th, 1st and nth harmonics are derived. To show the utility of this new element, example probelms have been solved and compared with the exact solution. The present element can be readily coded into any general purpose finite element program. © 1981.

Finite element analysis of the in-plane behaviour of annular disks

International Journal for Numerical Methods in Engineering

Lanczos versus subspace iteration for solution of eigenvalue problems

Dynamics of rotationally periodic structures

Computers & Structures

The truncated Lanczos algorithm for partial solution of the symmetric eigenproblem

Journal	Computers and Structures
ISSN	00457949
Open Access	No