Updating the quadratic asymmetric vibration system with no-spillover

Abstract

In this paper, the model updating problem of quadratic asymmetric vibration system with no-spillover is considered. Based on the spectral decomposition of a quadratic asymmetric pencil, the original quadratic asymmetric vibration system is updated to a new system such that some natural frequencies are replaced by some suitable chosen or newly measured ones, while the new system preserves no-spillover. The parametric solutions to the model updating problem of quadratic asymmetric vibration system are provided. When the system has repeated natural frequencies, a sufficient condition that the model updating problem can be solved is provided, and the performance of the proposed method is illustrated by some numerical examples.