Mode Tracking With Reduced Data Set In Structural Optimization

摘要

A new approach that uses the fourier Transform method to track the structural mode shapes and to detect the frequency crossing phenomenon in structural optimization is presented. Instead of using the mass orthogonality property of eigenvectors~1 or the higher order eigenpair perturbation~2 algorithm which both require the entire set of finite element data for any eigen mdoe, the proposed approach applies the Fourier Transform method to a subset of the finite element data and successfully identifies the switched modes. The size of the subset of finite element data is very small if only lower modes are of interest, and will grow to a full set as the number of modes of interest increases. Each eigen mode can be seen tagged with a mathematical 'label' through the proposed procedures, as a result the need of a human's visual inspection to identify desired eigen modes is reduced, if not eliminated. Mode tracking during the optimization process is accommplished through the usage of the Correlation Theorem which, by using the convolution procedure with a time lag, can indicate the similarity between two mode shapes. Two examples are provided to verify the proposed approach.