Bell-shaped proportional viscous damping models with adjustable frequency bandwidth. (February 2021)

• Record Type: Journal Article
• Authors: Lee, Chin-Long
• Is Part Of: Computers & structures. Volume 244(2021)
• Publication Date: 2021-02
• Subjects: Proportional damping model -- Bell-shaped basis function -- Sparse damping matrix -- Adjustable bandwidth -- High order series model -- Compound model; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2020.106423
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: Three modifications to improve recent series proportional damping model. Bell-shaped basis functions with adjustable bandwidths. Matching damping curves with drastic changes over short frequency intervals. Sparse block damping matrices with high computational efficiency. Same order of efficiency as the Rayleigh model. Abstract: A proportional viscous damping model based on a bell-shaped basis function parameterized by the frequency and damping ratio at its peak has recently been proposed. The basis function in the frequency domain has a fixed frequency bandwidth and could not match a damping ratio curve that changes precipitously over a short frequency interval. This study proposes new parameters to control the bandwidth, while maintaining the sparsity of damping coefficient matrix and the order of computational efficiency. Three types of modification are introduced. Types 1 and 3 control the bandwidth while maintaining the symmetry of the bell shape on the logarithmic scale, and Type 2 allows the left and right bandwidths to be adjusted independently. Type 3 controls the bandwidth while maintaining the same number of nonzeros in the expanded damping matrix, but the other two have the number of nonzeros increased for a smaller bandwidth. These modifications make the model versatile in matching any smooth damping ratio curve, particularly for a curve that has damping ratios changing drastically over a short frequency interval. Several examples are given to showcase their matching performance and the sparsity of their expanded damping coefficient matrices.