Structural Dynamics

A growing body of evidence suggests that limited accuracy can be expected from analytical and computational tools relying on linear viscoelasticity for the prediction of rolling resistance in real systems presenting material and geometric nonlinearities. A set of experimental data for the viscoleastic resistance to motion incurred by a rigid sphere rolling between two parallel sheets of rubber, in realistic in-service conditions, was determined, in a previous work (Zéhil and Gavin, 2019-A). The tests involved different elastomers (a Urethane rubber and a Neoprene rubber) and different sheet thicknesses, ball diameters, loading levels and rolling speeds. The accuracy of linear models in predicting such practical data is assessed in this work. To this aim, the elastomers are described by general linear viscoelastic models whose master-curves are characterized by: (i) High Frequency Thermo-Viscoelastic Spectroscopy, under very small strain amplitudes, and (ii) Dynamic Mechanical Analysis under relatively larger deformations. In both cases, rolling resistance predictions are obtained using computational tools based on linear viscoelasticity (Zéhil and Gavin, 2013-A,B) and compared to the measurements. Conclusions are drawn regarding: (i) the practical limitations of linear rolling resistance models, and (ii) influences of nonlinearities such as those due to large deformations, to the Mullins effect (Mullins, 1969) and to the Payne effect (Payne, 1962), on predictions.

This paper makes an interesting case for the need to consider mechanistic variations in rolling resistance forces due to non-coplanar surfaces and surface roughness. An experimental apparatus is designed to measure rolling resistance in the practically imperfect conditions of lightly-damped rolling isolation systems. These conditions include support compliance, surface imperfections and material inhomogeneities under relatively large loads. Rolling resistance experiments are conducted on steel balls between rubber sheets. Suitable mechanistic interpretations are provided for principal sources of variability. It is shown that measurement errors can be significant and that experimental results should be considered with caution. Suitable approaches for interpreting the results are then proposed and applied to this aim. Useful analytical models are fitted successfully to the processed data.

Rolling isolation systems (RISs) protect mission-critical equipment and valuable property from earthquake hazards by decoupling the dynamic responses of vibration-sensitive objects from horizontal floor motions. These responses involve the constrained rolling of ball bearings between bowl-shaped surfaces. The light damping of steel bearings rolling between steel plates can be augmented by adhering thin rubber sheets to the plates, increasing the rolling resistance and decreasing the displacement demand on the RIS. An assessment of the ability of lightly and heavily damped RISs to mitigate the hazard of seismically induced failures requires high-fidelity models that can adequately capture the systems' intrinsic nonlinear behavior. The simplified model presented in this paper is applicable to RISs with any potential energy function, is amenable to both lightly and heavily damped RISs, and is validated through the successful prediction of peak responses for a wide range of disturbance frequencies and intensities. The validated model can therefore be used to compute the spectra of peak floor motions for which displacement demands equal capacity. These spectra are compared with representative floor motion spectra provided by the American Society of Civil Engineers 7-10. The damping provided by rolling between thin viscoelastic sheets increases the allowable floor motion intensity by a factor of 2-3, depending on the period of motion. Acceleration responses of isolation systems with damping supplied in this fashion do not grow with increased damping, even for short-period excitations.

An assessment of the ability of lightly- and heavily-damped rolling isolation systems (RISs) to mitigate the hazard of seismically-induced failures requires high-fidelity models that can adequately capture the system’s intrinsic non-linear behavior. The light damping of steel bearings rolling between steel plates can be augmented by adhering thin rubber sheets to the plates, increasing the rolling resistance and decreasing the displacement demand on the RIS. The simplified model discussed in this paper is applicable to RISs with any potential energy function, is amenable to both lightly- and heavily damped RISs, and is validated through the successful prediction of peak responses for a wide range of disturbance frequencies and intensities. The damping provided by rolling between thin viscoelastic sheets increases the allowable floor motion intensity by a factor of two-to-three, depending on the period of motion. Acceleration responses of isolation systems with damping supplied in this fashion grow with increased damping, at short-period excitations.