Dynamic Simulation of Structures with Nonlinear Vibration Isolators: A Data-Driven Approach for Random Vibration

Background: The vibration isolator is the core component ensuring stable operation of precision equipment under severe vibration conditions. Efficient and accurate simulation of isolator-integrated structures is crucial for optimizing vibration isolation design and enhancing equipment adaptability. However, effectively addressing the nonlinear characteristics of isolators in random vibration analysis remains a major challenge. A key difficulty lies in establishing constitutive relationships for isolators under random vibration conditions. Existing indirect modeling approaches based on non-random test data often yield unpredictable errors due to discrepancies between test and actual service conditions. Methods: This study proposes a direct method utilizing random vibration test data for constitutive modeling and subsequent simulation. Furthermore, by leveraging the structural characteristic that only isolators exhibit nonlinearity while other components remain linear, the algorithm is optimized through an integrated approach involving statistical linearization, dynamic substructuring, pseudo-excitation, and fixed-point iteration methods. Results: The proposed method achieves random vibration simulation efficiency comparable to purely linear methods while delivering a fourfold improvement in accuracy. The effectiveness of the approach is successfully validated through two numerical examples. Conclusions: The results confirm that the proposed direct constitutive modeling and optimization strategy offers improved error controllability, providing a reliable and robust tool for the simulation and design of vibration isolation systems.