Nonlinear inertial amplifier resilient friction base isolators for multiple degrees of freedom systems

This study introduces the nonlinear inertial amplifier resilient friction bearing isolators (NIARFBI). Another friction base isolator, namely the nonlinear inertial amplifier friction pendulum system (NIAFPS), is derived by eliminating the static damping from the governing equation of motion of the NIARFBI. The damping for NIAFPS is generated through the motion of the friction element of the isolator during the movement of the base layer. These novel isolators are placed at the base of the multiple degrees of freedom (MDOF) systems to reduce their dynamic responses. Every element of the highly nonlinear governing equations of motion of the dynamic systems isolated by each nonlinear isolator is linearized using the stochastic linearization approach. The specific mathematical formulation for the optimal design parameters for each nonlinear isolator is derived using the H-2 optimization approach. In order to determine the dynamic responses analytically, the transfer function is established. The dynamic responses of the novel isolators are compared with the dynamic responses of the traditional isolators. Accordingly, the displacement reduction capacities of optimum NIARFBI and NIAFPS are significantly 93.60% and 70.82%, superior to TRFBI and TFPS. The acceleration reduction capacities of optimum NIARFBI and NIAFPS are 88.27% and 58.92% superior to TRFBI and TFPS. The recently developed expressions for this study are all mathematically accurate and applicable for practical applications.

Automated summary

This study presents two novel friction-based isolators, NIARFBI and NIAFPS, which are placed at the base of multiple degrees of freedom (MDOF) systems to reduce their dynamic responses. The design parameters for each isolator are derived using the H-2 optimization approach, and the dynamic responses are analyzed using the established transfer function. The results show that the displacement and acceleration reduction capacities of the optimum NIARFBI and NIAFPS are significantly superior to the traditional FRBI and FPS.