Hermite Polynomial Chaos Expansion Method for Stochastic Frequency Response Estimation Considering Modal Intermixing

Abstract eng:
The frequency response shows a big significance in estimating the structural response of linear systems subjected to dynamic loads. Its quantification is decided by the modal properties (e.g. natural frequencies and mode shapes), which are always involved in the random eigenvalue problem regarding uncertain structures. The conventional way to determine the associated stochastic frequency response (SFR) is the directly sample-based method (DSBM), which relays on Monte Carlo sampling technique and deterministic modal analysis by FEA. However, the accuracy of the DSBM is at the cost of efficiency since a large number of modal analyses are required. In this work, the Hermite polynomial chaos expansion method (HPCEM) is implemented to solve the random eigenvalue problem. The coefficients are estimated by the least square method (LSM) considering its robustness and facility. Furthermore, the modal intermixing problem is particularly considered whereby the mathematical limitation and physical validity of the HPCEM are specified. In order to fulfill the practical requirements, a univariable based strategy is proposed to avoid this issue. This strategy in conjunction with the modal assurance criterion (MAC) provides a quantitative way to define the modal intermixing. The fast modal solutions by the HPCEM will be helpful to control the dynamic response within certain frequency interval of interest during the design phase, on one hand; on the other hand, the HPCEM can also be used to evaluate the dynamic response and thereafter to improve efficiency of reliability analysis. Numerical investigations of the SFR provide the comparisons between the results obtained by the HPCEM and DSBM, which demonstrate the efficiency and accuracy.

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