The Optimum Enhanced Base Isolators Applied to MDOF Systems: Exact Closed-Form Expressions

Purpose The dynamic response reduction capacities of conventional base isolators applied to multi degrees of freedom systems can be increased by adding inerters and resonators inside their core materials. The drawbacks/limitations of conventional base isolators can also be overcome using inerters and resonators. However, the existing literature lacks application of inerter base isolators, grounded resonating base isolators, and ungrounded resonating base isolators for multiple degrees-of-freedom (MDOF) systems to control dynamic responses. Additionally, exact-closed form expressions for optimal design parameters for these novel isolators applied in the MDOF system do not exist. Accordingly, two research gaps are found. Therefore, to address the research gaps, the inerter base isolators (IBI), grounded resonating base isolators (GRBI), and ungrounded resonating base isolators (URBI) are introduced in this paper to mitigate the dynamic responses of the multi degrees of freedom systems (MDOF). Methods The mathematical closed-form solutions for optimal design parameters for IBI, GRBI, and URBI for MDOF systems are derived using the H-2 optimization technique. The dynamic responses of the uncontrolled and controlled MDOF systems are derived using transfer matrix formation. The dynamic response reduction capacities of the optimum novel isolators are compared with the dynamic response reduction capacities of the conventional base isolators (BI). Results From the parametric study, it has been found that higher isolator and inerter mass ratios are recommended for optimum IBI, whereas higher isolator and moderate resonator mass ratios are recommended for optimum GRBI. In addition, for optimum URBI, a higher isolator mass ratio is recommended. The dynamic response reduction capacities of optimum IBI, GRBI, and URBI are 93%, 95.34%, and 92.93%, greater than the optimum BI for five degrees of freedom systems. In contrast, the dynamic response reduction capacities of optimum IBI, GRBI, and URBI are 96.69%, 98%, and 96.59%, greater than the optimum BI for ten degrees of freedom systems. Conclusions The study suggests that higher isolator and inerter mass ratios are recommended for optimal IBI, while higher isolator and moderate resonator mass ratios are recommended for GRBI. For URBI, a higher isolator mass ratio is also recommended. The dynamic response reduction capacities of optimum IBI, GRBI, and URBI are 93%, 95.34%, and 92.93% higher than the optimum BI for five degrees of freedom systems, and 96.69%, 98%, and 96.59% higher than the optimum BI for ten degrees of freedom systems.

Automated summary

This paper introduces the application of inerter base isolators, grounded resonating base isolators, and ungrounded resonating base isolators in mitigating the dynamic responses of multi degrees of freedom (MDOF) systems. The mathematical closed-form solutions for the optimal design parameters of these novel isolators in MDOF systems are derived using the H-2 optimization technique. The dynamic response reduction capacities of the novel isolators are found to be higher than those of conventional base isolators.