Optimal Design and Practical Considerations of Tuned Mass Dampers for Structural Control

Optimal Design and Practical Considerations of Tuned Mass Dampers for Structural Control

Chi-Chang Lin (National Chung Hsing University, Taiwan, R.O.C.) and Jer-Fu Wang (National Museum of Natural Science, Taiwan, R.O.C.)
DOI: 10.4018/978-1-4666-2029-2.ch006
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The design concept and procedure for tuned mass dampers (TMDs) have been extensively investigated through numerical simulation analyses and experimental tests. Sophisticated three-dimensional building models were developed to examine the optimum installation location in elevation and in plane, number and movement direction of the TMDs with the consideration of translation-torsion coupling and soil-structure interaction effects. Analytical and empirical formulas were also derived to determine the optimal parameters of TMD. It is well recognized that the performance of a TMD is sensitive to the slight deviation of frequency ratio between the TMD and the structure. Multiple tuned mass dampers (MTMDs) were proposed to reduce this detuning effect. It is also recognized that TMD’s performance relies on its large stroke which may not be allowed due to the limitation of space and vibration components. The authors presented a two-stage optimum design procedure for MTMDs with limitation of their strokes. New invention patents both in Taiwan and in USA have been granted for the MTMD device.
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A TMD is a single-degree-of-freedom (SDOF) dynamic system. The design of TMD is to determine its mass, damping coefficient, and stiffness coefficient based on the characteristics of primary structure to which it is installed and/or the external excitation. The time-domain equations of motion of a linear structure-TMD system involves second-order differential. In the early stage, the application of TMD mainly focused on the vibration problem of mechanical systems. Although the concept of TMD dated back to 1909 (Frahm, 1911), Den Hartog (1956) could be the first one who provided a detail description and design formulas for TMD.

Den Hartog’s Design Formulas for Undamped Structures

In Den Hartog’s study, an undamped SDOF dynamic system subjected to sinusoidal loading was considered. For a given mass ratio of TMD to the primary structure, μ, he suggested that the optimal frequency ratio of the TMD to the primary, , and the optimal damping ratio of TMD, , can be calculated by the following equations


From Equation (1), the physical parameters (e.g., mass, damping coefficient, and stiffness coefficient) of a TMD can be obtained if the mass and natural frequency of the primary structure are given. Although the design problem is significantly simplified, it appears that the damping ratio of the primary structure is unrelated to the design of a TMD. As a result, the applicability of the equation to damped structures is not clear. The equation also implies that the larger the TMD mass, the smaller the value of . It is a reasonable situation because a larger TMD mass means larger system mass which will have a smaller resonant frequency to which a TMD is tuned.

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