The Optimum Inertial Amplifier Tuned Mass Dampers for Nonlinear Dynamic Systems
Abstract
The optimum inertial amplifier tuned mass dampers (IATMD) for vibration reduction of linear and nonlinear dynamic systems are introduced in this paper. H2 and H∞ optimization methods are applied to derive the exact closed-form expressions for optimal design parameters such as frequency and viscous damping ratios in simplified form mathematically for IATMD. From the parametric study, using these optimal closed-form solutions, a higher damper mass ratio, a higher amplifier mass ratio, and a lower inertial angle are recommended to design optimum IATMD to achieve robust dynamic response reduction capacity having moderate viscous damping and lower frequency ratios at an affordable range. The optimum IATMD systems are installed on top of linear and nonlinear single-degree-of-freedom systems to mitigate their dynamic responses of them. The linear dynamic responses are determined through transfer matrix formations, and nonlinear dynamic responses are derived using the harmonic balance (HB) method. H2 optimized IATMD is significantly 44.78 and 48.62 superior to the H2 optimized conventional tuned mass damper one (CTMD1) and conventional tuned mass damper two (CTMD2). Furthermore, H∞ optimized IATMD is significantly 39.98 superior to the H∞ optimized conventional tuned mass damper (CTMD). According to the nonlinear dynamic analysis, H2 optimized IATMD systems are significantly 35.33, 76.97, and 35.33 superior to the H2 optimized CTMD. Furthermore, H∞ optimized IATMD systems are significantly 25.92, 73.64, and 25.92 superior to the H∞ optimized CTMD. The results of this study are mathematically accurate and feasible for practical applications.
