Virtual High-Order Model Reduction Method for Vibration Modal Analysis

The vibration modal analysis of large-scale structures typically requires significant computational costs. The high-order model reduction (HOMR) is a recently developed approach that can save computational costs and quickly obtain structural vibration modal parameters. However, this method has the drawback of requiring the inversion of the mass matrix, which can lead to computational inefficiency. In this work, a virtual HOMR method is proposed to avoid the inversion of the mass matrix, thereby further saving computational costs. The proposed method consists of two steps to solve for the eigensolutions of the original system. Firstly, HOMR is utilized to solve for the eigenvectors of a virtual system where the mass matrix is the identity matrix. Then, the obtained eigenvectors of the virtual system are taken as the initial iterative values, and the subspace iteration method is applied to obtain the eigensolutions of the original system. Three examples are used to validate the proposed virtual HOMR method. The computational results demonstrate that, compared to the iterated improved reduced system (IIRS) method and the original HOMR method, the newly introduced method exhibits the highest levels of computational efficiency and accuracy. Furthermore, the proposed method boasts a unique advantage that other model reduction techniques do not possess: it can still yield highly accurate calculation results even when the arrangement of master degrees of freedom is poorly designed.