Type 4 bell-shaped proportional damping model and energy dissipation for structures with inelastic and softening response

• Published in: Computers & structures Vol. 258; p. 106663
• Main Author: Lee, Chin-Long
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.01.2022; Elsevier BV
• Subjects: Basis functions; Damping ratio; Earthquake dampers; Energy dissipation; High order compound model; Mathematical models; Modal damping; Negative stiffness; Parameters; Proportional damping model; Seismic response; Softening; Softening response; Sparse damping matrix; Sparse matrices; Stiffness; Negative stiffness; Softening response; Energy dissipation; Proportional damping model; Sparse damping matrix; High order compound model
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2021.106663

•Address concerns of proportional damping model with tangent stiffness.•Relate damping ratio and energy dissipation for inelastic response.•High order compound model matching damping ratio for inelastic response.•Versatile for arbitrary damping ratio, particularly for softening response.•Sparse block damping matrices with high computational efficiency. Several damping models were proposed to incorporate un-modeled damping when simulating seismic response of large-scale structures, but most did not provide parameter calibration against energy dissipation. This study addresses this problem by developing a new bell-shaped proportional damping model, allowing energy dissipation to be directly related to modal damping ratio. It also addresses the concerns of using proportional damping models with the tangent stiffness approach. The relationships between energy dissipation and damping ratio for inelastic response, including hardening, softening, and perfectly-plastic response, are established analytically. The new model, named as Type 4, is a high order compound model extended from Type 2 and Type 3 models recently proposed. With five parameters, its bell-shaped basis function allows users to match any desired damping ratio curve in the frequency domain, particularly those corresponding to negative stiffness. It allows the damping ratio for inelastic response to be independent of damping ratio for elastic response, a flexibility not commonly found in existing models. Its damping matrix allows sparse matrix implementation and maintains the same order of computational cost as Rayleigh model. In this model, the relationships between damping forces and rate of constitutive forces appear as bell-shaped curves, thereby avoiding spurious damping forces.