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. [Formula: see text] and [Formula: see text] 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. [Formula: see text] optimized IATMD is significantly [Formula: see text] and [Formula: see text] superior to the [Formula: see text] optimized conventional tuned mass damper one (CTMD1) and conventional tuned mass damper two (CTMD2). Furthermore, [Formula: see text] optimized IATMD is significantly [Formula: see text] superior to the [Formula: see text] optimized conventional tuned mass damper (CTMD). According to the nonlinear dynamic analysis, [Formula: see text] optimized IATMD systems are significantly [Formula: see text], [Formula: see text], and [Formula: see text] superior to the [Formula: see text] optimized CTMD. Furthermore, [Formula: see text] optimized IATMD systems are significantly [Formula: see text], [Formula: see text], and [Formula: see text] superior to the [Formula: see text] optimized CTMD. The results of this study are mathematically accurate and feasible for practical applications.