Sparse proportional viscous damping model for structures with large number of degrees of freedom

• Published in: Journal of sound and vibration Vol. 478; p. 115312
• Main Author: Lee, Chin-Long
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 21.07.2020; Elsevier Science Ltd
• Subjects: Basis functions; Bell-shaped basis function; Cholesky factorization; Computational efficiency; Conjugate gradient method; Curve fitting; Damping; Damping ratio; Degrees of freedom; Dynamic response; Frequencies; Iterative methods; Large number of degrees of freedom; Matrix; Proportional damping model; Soil analysis; Soil-structure interaction; Sparse matrix; Sparsity; Stiffness matrix; Symmetric positive definite; Vibration; Viscous damping; Well-conditioned matrix; Symmetric positive definite; Sparse matrix; Large number of degrees of freedom; Computational efficiency; Proportional damping model; Well-conditioned matrix; Bell-shaped basis function
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2020.115312

This paper proposes a proportional viscous damping model that is computationally very efficient for response history analysis of a large-scale structure with a large number of degrees of freedom. The proposed model is based on a bell-shaped basis function parameterized by the frequency and damping ratio at its peak. Any damping ratio curve in the frequency domain can be easily matched by adding several bell-shaped basis functions. Three methods based on least-squares curve-fitting are used to determine the model parameter values. This model allows for solving structural dynamic response using a sparse block matrix without approximation nor iterative refinement. The block matrix maintains the positive definiteness of the traditional effective stiffness matrix, allowing efficient solution methods such as Cholesky factorization and the conjugate gradient method for solutions. It also allows assigning different damping ratio curves to different structural zones, suitable for soil-structure interaction analysis. Its performance compared against existing damping models is particularly remarkable for large-scale structures with a large number of degrees of freedom in the order of thousands or even millions. The larger the number of degrees of freedom, the better the relative efficiency compared to existing damping models. Several examples are given to demonstrate this remarkable performance.