Model reduction and optimal parameters of mid-story isolation systems

• The development of a modal synthesis based reduced order model for mid-story isolators.
• Analytical formulation for optimal parameter estimation of mid-story isolation systems.
• Effect of isolation system placement in buildings.
• Response reducing effectiveness of mid-story isolation systems.

The paper presents a modal synthesis-based approach to develop a reduced two, three, or higher order model to represent a mid-story isolated building structure. Herein, the approach is utilized to obtain a simple two-degree of freedom model which can effectively capture the response characteristics of the full system well. This reduced order model is used to formulate analytical approaches for calculating the optimal parameters of a mid-story isolation system that either minimize the (a) maximum base shear force amplitudes for harmonic base excitations or (b) base shear force variance for a band-limited white noise random base excitation. Numerical examples are, then, presented to study the influence of the placement of an optimal mid-story isolation system at different levels in a building as well as to show the structural response reducing effects of the isolators.