A new eigensolution of a combined primary-secondary structure system via the improved iteration order reduction method (IIOR)

The interaction between primary structures and non-structural components (NSCs) is an essential factor in accurately estimating the eigensolutions of coupled structural systems. Neglecting this interaction can lead to significant inaccuracies. This study introduces a novel algorithm, the improving iteration order reduction (IIOR) method, which effectively incorporates these interactions. The IIOR method combines dynamic condensation with perturbation techniques in an iterative framework, allowing for the precise computation of eigensolutions for the coupled system from the respective eigensolutions of the primary and secondary structures. By introducing deviation eigenvalues, the algorithm significantly enhances both the convergence and convergence rate of the iterative process. This method is independent of the size of the master degree of freedom, making it suitable for the design of NSCs in large-scale or complex structures. The proposed technique's effectiveness and accuracy are rigorously verified through theoretical analysis and numerical simulations, using a multi-degree-of-freedom primary structure with various types of NSCs. Additionally, the IIOR method demonstrates superior computational efficiency compared to other traditional iterative methods such as the iterated improved reduced system (IIRS) method, iterative order reduction (IOR) method, and subspace iteration method (SIM), etc.