Impacts of the weight coefficient and modal assurance criterion of large structures on observation station selection and optimization

Abstract

Considering the shortcomings of the modal assurance criterion in the observation station selection and optimization algorithm for the structural modal testing experiment, this paper proposed a new criterion on the basis of the rule that the vibration mode is weighted-orthogonal to the mass. Since the vibration distributions of modes for large-scale structures vary from one another, the contribution of the high-order modes to the modal strain energy cannot be neglected. Therefore, a weight coefficient representing the contribution ratio of the high-order modal was introduced to modify the modal matrix. In addition to that, a hybrid optimization algorithm based on effective independence method and the weighted average modal strain energy coefficient method based on the effective independence method were proposed. Calculations guided by two-degree freedom system equal mass and non-equal-mass theories were initiated and comparisons and contrasts were made for the above-mentioned two methods, the average mode strain energy coefficient method based on the effective independence method and the weighted average modal strain energy coefficient method based on effective independence method through Garteur simulation tests to examine the differences in their resultant observation station arrangements. Results have shown that the traditional mode assurance criterion could not be used to judge whether the modes are weighted orthogonally or not when various nodes differ in their masses, but the new criterion involved in this paper could. The introduction of the weight coefficient effectively averted the aggregation of observation stations, best ensured the contributions of all the modal strain energy and fulfilled what’s required by a preferred observation station arrangement. Model tests were also conducted by employing the Garteur plane to test the weighted average mode energy coefficient method based on the effective independence method with the new modal assurance criterion proposed. It was found that the new modal mode assurance criterion guaranteed the completeness and linear independence of the monitoring mode, and that the weight coefficient introduced effectively magnified the contributions of the high-order modes to the modal strain energy, improved the accuracy of the test results. In the final analysis, the new assurance criterion is of great practical value to the observation station optimization and large-scale structure distribution. The method proposed in this paper has been applied to the modal test of a large carrier rocket and an observation station layout optimization software of large structural modes has been developed based on MATLAB language. It has been validated that this algorithm has faithfully guaranteed the integrity and linear independence of the modes monitored and that it can ensure the optimization and arrangement of observation stations in the modal test of large and complex structures.