Issue: 2(38), 2015. Series: Multi-Topic

ALGEBRAIC PROBLEM OF EIGENVECTOR AND EIGENVALUES OF HIGH ORDER IN TASKS OF DYNAMICS AND STABILITY OF A CONSTRUCTION

UDK: 624.042

Ignat'ev V. A., Romashkin V. N.

The authors carry out a comprehensive review of methods for reduction of the order and solution of generalized algebraic problem of eigenvalue and eigenvector of high order which occur when using finite element method and method of movement to the solution of the task of structural mechanics on free vibrations and stability. Solution of the eigenvalue problem might be found in a large number of scientific works, both foreign and domestic authors, mainly differ in the way of construction of the subspace of basis vectors. Among these works iterative and reduction methods which are used by various schools and groups of researches are clearly distinguished. In this study, arrangement, classification and analysis of these methods are performed. The goal is to provide wide and structured outlook at the current situation in this field of research.