The exact closed-form expressions for optimal design parameters of resonating base isolators

Abstract

In this paper, the exact closed-form analytical expressions of the optimal design parameters for two different base isolation (BI) configurations, i.e., grounded (GR-BI) and ungrounded (UR-BI), are derived employing H2 and H∞ optimization methods. To compare the performance of resonating isolators fairly with an equivalent base isolator, an additional mass is added to the base isolator’s mass. Frequency domain and time history analysis have been conducted to obtain each isolator’s exact vibration reduction capacity. Results from frequency domain analysis show that H2 optimized ungrounded resonating base isolator has a negligible effect on the vibration mitigation compared to the equivalent base isolator having equal total mass. The response reduction capacity of the GR-BI is significantly 23.81% superior to the BI and UR-BI both while implementing H2 optimization method. On the other hand, for H∞ optimization, the response reduction capacity of the GR-BI is significantly 26.1% and 34.98% superior to the BI and UR-BI, respectively. Subsequently, numerical studies employing the Newmark-beta method have been conducted to obtain time-domain responses using near-field earthquake base excitations. Results from time history analysis depict that the response reduction capacity of H2 optimized GR-BI is significantly 47.80% and 47.51% superior to the response reduction capacity of H2 optimized BI and UR-BI. In contrast, the response reduction capacity of H∞ optimized BI is significantly 56.45% and 43.75%, superior to the response reduction capacity of H∞ optimized UR-BI and GR-BI. However, the response reduction capacity of H∞ optimized GR-BI is significantly 22.58% superior to the response reduction capacity of H∞ optimized UR-BI. The requirement of the damping ratios of all the proposed isolators are within unity; hence these are affordable. The results are mathematically accurate and feasible for practical design purposes.