Optimal negative stiffness inertial-amplifier-base-isolators: Exact closed-form expressions

Abstract

This paper introduces the concept of negative stiffness inertial-amplifier-base-isolators to achieve enhanced broadband vibration control. Three physically different novel isolators, namely inertial amplifier base isolator (IABI), negative stiffness inertial amplifier base isolator (NSIABI), and negative stiffness base isolator (NSBI), are achieved only by tuning a single system parameter, namely the mass tuning ratio for novel isolators γ. The exact closed-form expressions for the optimal system parameters, such as the frequency and damping ratio of the novel isolators, have been derived analytically using H2 and H∞ optimization methods. The response reduction capacity of each optimized novel isolator has been compared with the optimized traditional base isolator (TBI). Results showed that the vibration reduction capacity of H2 optimized NSBI, NSIABI, and IABI is significantly 73.02%, 75.55%, and 76.48 %, superior to the TBI. While, the vibration reduction capacity of H∞ optimized NSBI, NSIABI, and IABI is significantly 69.69%, 73.67%, and 77.37% superior to the TBI. Overall all three novel base isolators have at least 69% more vibration reduction capacity than traditional base isolators, respectively. These novel isolators are cost-effective and can provide superior vibration reduction capacity than other existing traditional base isolators, respectively.