The exact closed-form equations for optimal design parameters of enhanced inerter-based isolation systems

Abstract

This paper introduces the enhanced inerter-based isolation system (EIBI) to improve broadband vibration control. Using the H₂ optimization method, the exact closed-form expressions for the optimal design parameters of the EIBI, such as the frequency and viscous damping ratio, have been derived analytically. The optimal frequency and viscous damping ratios of EIBI decrease as the mass ratio of the EIBI increases. For optimal design purposes, the optimal viscous damping ratio of EIBI lies between 0.20 < ζ _b < 0.30, which is practically affordable and precise to implement. The exact closed-form expressions for optimal design parameters for traditional base isolators (TBI) have also been derived using the H₂ method to make a fair comparison with EIBI. When the base mass ratio of TBI increases, its optimal frequency and viscous damping ratios decrease. The response reduction capacity of each optimized novel isolator was compared to the response reduction capacity of each optimized TBI. Analysis of the frequency domain demonstrates that the response reduction capacity of the proposed EIBI is significantly 2.77% and 17.46% greater than that of the TBI subjected to harmonic and random white-noise base excitations. To verify the accuracy of the optimal closed-form expressions derived for each isolator using near-field earthquake base excitations, a numerical study employing the Newmark-beta method has been conducted. Hence, the time-history analysis reveals that the displacement and acceleration reduction capacities of EIBI are significantly superior to that of the TBI subjected to near-field earthquake base excitations by 12.86% and 24.61%, respectively. The EIBI systems are cost-effective and have greater vibration reduction capacities than TBIs.