Inerter-based vibration absorbers (IVAs) have been widely studied for the vibration control of multi-degree-of-freedom (MDOF) structures. Common analytical optimization strategies of IVAs for controlling the modal response of a specific mode neglect the contributions from non-resonant modes (denoted as modal interaction effects hereafter), which could weaken the validity of the optimum solution, while directly employing numerical search methods usually implies expensive computational costs in repeatedly evaluating control objectives under different sets of IVA parameters. To aim at both accuracy and efficiency of optimum design solution of IVAs for targeted modal response control, the Sherman-Morrison inversion (SMI) is exploited in this paper to derive explicit expressions of frequency response functions (FRFs) of IVA-controlled structures based on an MDOF model established in modal coordinates. In this way, the non-zero off-diagonal elements and precise expressions of diagonal elements in the FRF matrix are explicitly incorporated in the design process, with full account for modal interaction effects. The SMI is further implemented to calculate the FRF matrix of structures controlled by multi-IVA (MIVA) in an iterative manner, and subsequently, design strategies for targeted modal control using (M)IVA are proposed with particular focuses on wind-resistance and seismic design. Based on a high-rise building taken as the case study, the accuracy and efficiency in calculating the FRF matrix are quantitively assessed by Monte Carlo simulations. Two design examples, i.e., using a single tuned inerter damper (TID) for wind-resistance design and using a multi-TID for seismic design, are presented to validate the precision and efficiency of proposed design strategies. The results indicate that modal interaction effects are increasingly important for the design of (M)IVAs having larger inertance or being tuned to higher modes.
Targeted modal response control of structures with inerter-based vibration absorbers considering modal interaction effects
De Domenico D.;
2023-01-01
Abstract
Inerter-based vibration absorbers (IVAs) have been widely studied for the vibration control of multi-degree-of-freedom (MDOF) structures. Common analytical optimization strategies of IVAs for controlling the modal response of a specific mode neglect the contributions from non-resonant modes (denoted as modal interaction effects hereafter), which could weaken the validity of the optimum solution, while directly employing numerical search methods usually implies expensive computational costs in repeatedly evaluating control objectives under different sets of IVA parameters. To aim at both accuracy and efficiency of optimum design solution of IVAs for targeted modal response control, the Sherman-Morrison inversion (SMI) is exploited in this paper to derive explicit expressions of frequency response functions (FRFs) of IVA-controlled structures based on an MDOF model established in modal coordinates. In this way, the non-zero off-diagonal elements and precise expressions of diagonal elements in the FRF matrix are explicitly incorporated in the design process, with full account for modal interaction effects. The SMI is further implemented to calculate the FRF matrix of structures controlled by multi-IVA (MIVA) in an iterative manner, and subsequently, design strategies for targeted modal control using (M)IVA are proposed with particular focuses on wind-resistance and seismic design. Based on a high-rise building taken as the case study, the accuracy and efficiency in calculating the FRF matrix are quantitively assessed by Monte Carlo simulations. Two design examples, i.e., using a single tuned inerter damper (TID) for wind-resistance design and using a multi-TID for seismic design, are presented to validate the precision and efficiency of proposed design strategies. The results indicate that modal interaction effects are increasingly important for the design of (M)IVAs having larger inertance or being tuned to higher modes.Pubblicazioni consigliate
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