关键词:
Eigenvalues and eigenfunctions
摘要:
Due to the frequency-dependent characteristics of viscoelastic damping mechanical systems, solving their eigenvalues is highly challenging, especially for large-scale mechanical systems characterized by multiple damping models. A mechanical system with multiple damping models was taken as the research object, and an eigenvalue dimension reduction method based on physical subspace was proposed to achieve highly precise and efficient prediction of modal frequencies and vibration shapes. Firstly, multiple damping models were transformed into a unified rational fraction form, constructing a general damping system with a consistent and concise form. Next, utilizing the unified form, a physical space with the same dimension as the system was constructed, enabling the recursive generation of the physical subspace. By combining the state space with the Krylov subspace to derive the physical subspace, a dimension reduction method for eigenvalue solving based on the physical subspace was proposed, effectively addressing the issue of dimensionality explosion in traditional state-space representations for systems with multiple damping models. The theoretical and numerical analyses demonstrate that the proposed method offers superior efficiency and accuracy compared to conventional state -space -based dimension reduction approaches. © 2025 Chinese Vibration Engineering Society. All rights reserved.