An iterative reduced-order substructuring approach to the calculation of eigensolutions and eigensensitivities

Abstract

Substructuring methods are efficient to estimate some lowest eigensolutions and eigensensitivities of large-scale structural systems by representing the global eigenequation with small-sized substructural eigenmodes. Inclusion of more substructural eigenmodes improves the accuracy of eigensolutions and eigensensitivities, whereas decreases the computational efficiency adversely. This paper proposes a new iterative reduced-order substructuring method to calculate the eigensolutions and eigensensitivities of the global structure. A modal transformation matrix, relating the higher modes to the lower modes, is derived to transform the original frequency-dependent matrices of each substructure into frequency-independent ones. A simplified reduced-order eigenequation is then obtained through a few iterations performed on the modal transformation matrix and mass matrix. The eigensolutions and eigensensitivities of the global structure are calculated accurately with a small number of substructural eigenmodes retained, avoiding the inclusion of numerous substructural eigenmodes. Applications of the proposed method to a numerical frame and a practical large-scale structure demonstrate that the eigensolutions and eigensensitivities of the global structure can be calculated accurately with only a small number of substructural eigenmodes and a few iterations.