Friction-based elastic damping for dynamic analysis of structures
Author: John Timothy O’Hagan
Paper number: 410
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in Civil Engineering was accepted as a final report and is available on request - please contact research@eqc.govt.nz for access.
Abstract
The main objective of this Thesis is to improve the modelling of elastic damping in dynamic analysis of multi-degree-of-freedom systems undergoing inelastic response. Previous studies have shown that the elastic damping in a structure is not viscous in nature, but viscous damping can be carefully set up to achieve adequate performance in inelastic analyses.
Several existing alternative elastic damping models are investigated for their applicability to inelastic analyses. Coulomb friction-based damping forces are shown to produce equivalent viscous modal damping ratios that are amplitude dependent, frequency dependent and coupled. Simplified elastic analysis techniques are developed to determine the modal damping ratios when multiple modes are vibrating simultaneously at different amplitudes. This study utilises a collection of stiction elements which comprise of a spring and a Coulomb friction element in series. Three stiction elements in parallel between adjacent degrees-of-freedom can replicate damping ratios that are approximately independent of amplitude.
The three-element stiction damping model with reduced structural stiffness is the damping model most suited to inelastic analysis of both single and multi-degree-of-freedom systems. The model successfully emulates the effects of viscous damping in elastic analyses while having minimal artefacts on the engineering demand parameters of inelastic systems. Reduced stiction damping is superior to viscous damping because viscous damping must balance minimising the influence of mass-proportional damper forces with the magnitude of the elastic fundamental mode damping ratio.
A secondary aim of the study is to develop a damping model that can implement amplitude dependent damping ratios. A novel implementation of viscous damping, Improved Modified Viscous Damping, is developed to provide uncoupled, individual mode amplitude dependent damping ratios. The key to the new model is to scale the viscous damper coefficient in proportion to the instantaneous total energy in the system. Amplitude dependent damping is shown to have negligible effect on the peak response of inelastic systems.
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