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This study is focused on robust design optimization (RDO) of the tuned mass dampers (TMDs), which are widely used as a passive vibration controller in structural systems. The performance of the TMDs designed under the implicit assumption that all relevant system parameters (such as loading and structural characteristics) are deterministic is greatly affected by the inevitable inherent uncertainties in the system parameters. In this regard, a framework is proposed for the RDO of TMDs to determine its optimal solution which is less sensitive to system parameter variability. RDO is defined as a multi-objective optimization problem that aims to minimize the mean and variance of the performance function. In the case of multiple TMDs, the proposed framework uniquely avoids the presumption of their mass distribution, number, and placement location. In the proposed RDO framework, an augmented formulation is adopted wherein the design parameters are artificially introduced as uncertain variables with some prescribed probability density function (PDF) over the design space. The resulting optimization problem is solved using the stochastic subset optimization (SSO) and KN, a direct search optimization method. The effectiveness of the proposed framework is studied by analyzing four illustrative examples involving a single TMD attached to a single-degree-of-freedom (SDOF) structure, a single TMD attached to a multiple-degree-of-freedom (MDOF) structure, multiple TMDs attached to an MDOF structure, and an 80-story structure equipped with multiple TMDs.

The floors of large-span cantilever structure are easier to vibrate excessively due to relatively small structural rigidity. The tuned mass damper (TMD) is used to control human-induced vibration of the large-span cantilever structure floors. This paper describes a finite element model of large-span cantilever structure based on an example from building engineering. If the pedestrian frequency is equal to or half of the structural frequency, resonance will occur and the acceleration response will be maximized. The paper focuses on the parameters of tuned mass dampers to vibration serviceability when the frequency of walking excitation is equal to the structural frequency or half of it. It comes to such conclusions as follows. With the increase of TMD mass, the vibration reduction rate of TMD increases remarkably. When the total mass of TMD remains unchanged, the dispersion of TMD has little influence on the rate of vibration reduction. The error between the TMD frequency and the vertical natural frequency of the structure has a great influence on the effect of vibration reduction. With the increase of the error, the peak acceleration will increase and the rate of vibration reduction will decline. If the error is between -30%~30% and decreases sharply, then the downward trend of peak acceleration will slow down obviously.