Projection-based eigenproblem solver of large-scale viscoelastically damped systems via an original-dimension subspace

The analysis of frequency-dependent viscoelastic systems is computationally challenging, especially for large-scale structural systems with significantly different levels of damping. The focus of this research is to develop an efficient solver for eigenproblems of large-scale viscoelastic systems incorporating the widely-used standard linear solid models. The original- dimension subspace is proposed for the first time, which can provide enough information to directly deal with the eigenproblems of the original-dimension viscoelastic damped systems, instead of dealing with their corresponding linearized eigenproblems in a larger-sized state space. Using the concept of original-dimensional subspace, a direct basis-orthonormalized method is proposed to generate orthogonal basis. The direct basis-orthonormalized method can immediately generate the projection basis vector when generating an original dimension vector, avoiding the projection basis orthogonalization after generating the entire sequence. Based on the orthonormal basis in the original-dimensional subspace, the original-dimensional subspace method is proposed as a solver for the eigenproblem. Compared with the subspace methods based on the state space, the proposed original-dimension subspace method saves the linearization steps and preserves the original system structure. Through theoretical or numerical analysis, the proposed method requires less computational complexity and storage space and is therefore more efficient and accurate.