شينا ملكي

In structural engineering, complex systems often involve numerous degrees of freedom, which makes dynamic analysis difficult due to the high computational demands and time-consuming processes. Matrix condensation methods help reduce the complexity of the problem by eliminating less significant degrees of freedom and focusing on the more critical ones, allowing for faster and more efficient analyses. These methods simplify the system while maintaining the essential dynamic characteristics, making them essential for complex simulations with large datasets without a substantial loss of accuracy. However, the matrix condensation process can introduce uncertainties in predicting dynamic responses due to numerical approximations and simplifications in the model. These uncertainties primarily stem from the elimination of non-critical degrees of freedom and their effect on the behavior of the reduced system. Additionally, inherent uncertainties in structural parameters, such as material properties, can influence the accuracy of reduced-order models. Therefore, it is crucial to precisely assess the behavior of the reduced models during the condensation process and analyze the impact of structural uncertainties on the accuracy of dynamic predictions. eva‎luating the reliability of the results obtained from these methods can also contribute to improving model order reduction techniques and mitigating the effects of uncertainties. The analysis results revealed that the performance of model order reduction methods under uncertainty depends on the primary degrees of freedom retained during the reduction process, the structural characteristics, and the frequency range of the system. For structures with low-frequency ranges, simpler methods such as Guyan and dynamic showed good agreement with the full model and performed well in the lower modes. However, these methods demonstrated reduced accuracy in higher-frequency structures, particularly for higher modes. In contrast, advanced methods such as IRS and SEREP exhibited higher accuracy across all frequency ranges, particularly in higher frequencies and more complex structures, successfully predicting dynamic responses with strong alignment to the full model. These findings underscore the importance of correctly selecting key degrees of freedom and employing advanced methods to reduce the effects of uncertainties.

كاهش مرتبه مدل , كمي سازي عدم قطعيت ها , درجات آزادي اصلي , ويژگي‌هاي كليدي سازه , قابليت انطباق با مدل كامل

Model Order Reduction , Uncertainty Quantification , Master Degrees of Freedom , Structural Dynamic Features , Full Model Compatibility

Shina Maleki

Dr. Majid Ilchi Ghazaan