Optimum design parameters for a tuned-mass-damper to maximise the equivalent damping ratio

Tuned-Mass-Dampers (TMDs) are widely used to reduce structural vibrations and this paper examines the design parameters necessary for maximising the equivalent damping ratio which is often used in engineering practice to measure vibration reduction. This paper uses Fourier Response Functions to study the equivalent damping ratio based on a Single Degree-Of-Freedom (SDOF) system representing a structure and a Two Degree-Of-Freedom (TDOF) system representing the structure and a tuned-massdamper. By equating the maximum responses of the structures in the two systems, expressions for equivalent damping ratio can be derived. The mass ratio of the TMD to the structure is not a parameter for optimization as the objective function (the equivalent damping ratio) increases monotonically as the mass ratio increases. Thus the relationship between the objective function and the two design parameters, the frequency ratio of the TMD to the structure and the damping ratio of the TMD, can be determined and visualised without using particular optimization methods. Tables of the optimum parameters for TMDs and equivalent damping ratios are provided for design with typical structural damping ratios. An example of floor vibration induced by rhythmic crowd loads is provided to demonstrate the use of the optimum TMDs and the benefit of taking the equivalent damping ratio as the objective function in design for attenuating vibration.