Enhanced Rayleigh Damping Model for Dynamic Analysis of Inelastic Structures

Abstract

This paper presents an Enhanced Rayleigh damping model for dynamic analysis of inelastic structures. The conventional Rayleigh damping model has been extensively used to represent inherent energy dissipation sources in structures. However, when used in the analysis of inelastic structures, the Rayleigh damping model predicts unrealistically large damping reactions, a problem that has proven partially treatable by substituting the initial stiffness matrix with its tangent counterpart in the damping matrix formulation. However, using the tangent stiffness matrix in the Rayleigh damping model results in two major deficiencies, which are shown in this study to generate physically inadmissible responses: (1) negative definite damping matrices during softening, which produce destabilizing, as opposed to resisting, damping forces, and generate energy instead of dissipating it, thereby violating basic thermodynamics; and (2) instantaneous jumps—temporal discontinuities—in the damping reactions due to abrupt changes in the tangent stiffness matrix, which lead to numerical convergence failures. To eliminate these deficiencies, this study enhances the Rayleigh formulation by (1) eliminating the negative eigenvalues of element tangent stiffness matrices used to build the damping matrix, ensuring its positive semidefiniteness; and (2) introducing a first-order differential model that imposes continuous time variation of the element tangent stiffness matrices used to build the damping matrix, thereby ensuring temporal continuity of the damping reactions. Evaluation of the proposed damping model shows its effectiveness in eliminating the aforementioned deficiencies, while comparisons with other variations of the Rayleigh model demonstrate the effect of the aforementioned deficiencies on structural response predictions.