#5624. Type 4 bell-shaped proportional damping model and energy dissipation for structures with inelastic and softening response

August 2026publication date
Proposal available till 22-05-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Modeling and Simulation;
Civil and Structural Engineering;
Mechanical Engineering;
Computer Science Applications;
Materials Science (all);
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Abstract:
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.
Keywords:
Energy dissipation; High order compound model; Negative stiffness; Proportional damping model; Softening response; Sparse damping matrix

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