Effect of stiffness variability on the response of isolated structures

Results are presented of an investigation, the objective of which was to determine the relationship between the stiffness variability of the bearings of an isolation system and the response variability of the structure. The system is modeled as a rigid, rectangular structure that is free to translate and rotate. The isolation system consists of N isolation bearings arranged in a rectangular pattern, each with a stiffness ki that is an independent, normally distributed, random variable. Response spectrum analysis is used to obtain the analytical solution for the structure response. Approximate closed-form expressions are obtained for the variance of the centreline displacement, rotation, corner displacement and base shear, that are in terms of the variability of the isolator stiffness, aspect ratio of the structure, and the number and layout of isolation bearings. Results show that the standard deviation of the centreline displacement and base shear decrease with increasing number of isolation bearings, and are independent of the aspect ratio and layout of isolators, and in all cases are less than 1/4 the standard deviation of the isolator stiffness. The standard deviation of the corner displacement is a function of all of the system parameters, and is bounded below by the standard deviation of the centreline displacement and above by the standard deviation of a bar aligned perpendicular to the direction of ground motion with m isolation bearings distributed along the length. The approximate expressions are shown to be in good agreement with the results of Monte Carlo simulations. The results should be of use to designers of isolated structures and manufacturers of isolation systems, in assessing the significance of stiffness variability on the response of the isolated structure. Copyright © 2000 John Wiley & Sons, Ltd.