Dynamic reduction in the calculation of bridge structures

In modern bridge construction, on the one hand, there are increasing trends towards increasing bridge spans, which requires reducing the weight of structures. On the other hand, the use of structural elements made of various composite materials is expanding, which allows to significantly reduce the weight of the bridge structures as a whole. However, the creation of new forms of span structures of bridges requires more detailed calculations in order to optimize such forms, in particular the role of calculating the dynamic impact, because with increasing spans and weight loss, increases design flexibility and sensitivity to dynamic loads. In the present paper, the problems of solving an incomplete algebraic problem of eigenvalues and eigenvectors are considered. To increase the accuracy of the calculation and exclude the use of high-order matrices, a method of sequential reduction of the stiffness and equivalent mass matrices is proposed. The method is based on the construction of partial systems using a static transformation, followed by the solution of its own problem for the partial system. In the process of solving this problem through the eigenvectors of the system, the minor unknowns are reduced to the main ones. Dynamic reduction showed high calculation accuracy.