| dc.description.abstract | Damping forces are always present in real structures, occurring in several different forms, making them challenging to model expressly. Damping is often assumed to be viscous in nature, due to the simplicity of the mathematics, sometimes inappropriately when large friction forces are present.
This research aimed to determine a relationship between a friction-based single degree of freedom (SDOF) structure’s assumed equivalent viscous damping ratio and the coefficient of friction.
This research focused on mathematically modelling the dynamic response of a theoretical single-storey structure, behaving linear elastically, to an applied harmonic load in two different damping cases namely the common assumption of viscously underdamped and a friction damping case, using an alternative approach that simplifies the traditionally non-linear solution to a linear one.
The physical model was idealised as an SDOF spring-mass-damper system and the mathematics of the general solutions for this system’s responses to different damping cases and vibration types introduced. Notably covering the classic non-linear approach to friction damping, for comparison. The simplified response for the friction damped case under harmonic excitation, was derived from first principles by adapting a method proposed for free friction damped vibration.
The system’s response for a range of common viscous damping ratios are analysed. The same analysis being performed for a range of different friction coefficients.
Ultimately the damping ratios and friction coefficients are compared, those causing similar responses from the system were selected, and a simple initial relationship between the viscous and friction damped cases determined for the selected cases. | |
