Tuned tandem mass dampers-inerters with broadband high effectiveness for structures under white noise base excitations

Abstract

By integrating the tuned tandem mass dampers (TTMD) with two inerters, the tuned tandem mass dampers-inerters (TTMDI) with high effectiveness and wide frequency spacing (i.e., high robustness) have been proposed in this paper. It is expected that the frequency spacing of the TTMDI will be comparable with that of the multiple tuned mass dampers. In order to reveal the fundamental performance of the TTMDI, it is attached to a single degree of freedom (SDOF) structure under random Gaussian white noise base excitations. Closed-form expressions for calculating the dimensionless displacement variances are thereupon derived for the SDOF structure–TTMDI system. The optimization criterion is determined as the minimization of the dimensionless displacement variances. Employing the gradient-based optimization technique, the effects of varying the key parameters on the performance of the TTMDI are scrutinized in order to probe into its superiority. Evaluation of the performance of the TTMDI includes that of its effectiveness, strokes, stiffness, damping coefficient, distributions of the inertance coefficients, frequency spacing, and frequency response of the controlled structure. For purposes of further comparison, the optimum results of the TTMD and tuned mass damper-inerter (TMDI) are also included into consideration. Results clearly demonstrate that the TTMDI outperforms both the TTMD and TMDI because of several advantages, particularly high effectiveness and broadband characteristics. Therefore, the TTMDI is deemed to be a broadband high effectiveness control device. Furthermore, the TTMDI only needs a linking dashpot and is capable of decentralizing a large inertance coefficient, thus showing its simplicity and easier implementation.