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Abstract A numerical searching procedure to find the optimum tuning frequency and damping ratio of the tuned‐mass damper which can reduce the steady‐state response of damped main systems to a minimum level is developed and applied to the two different harmonic excitation sources, support motion of fixed‐displacement amplitude and support motion of fixed‐acceleration amplitude. The explicit formulae for these optimum parameters are then derived through a sequence of curve‐fitting schemes. It has been found that, as the error of the explicit formulae is negligible, they provide a convenient tool to compute the optimum parameters in engineering applications. The numerical results show that the tuned‐mass damper is less effective in reducing the system's response when there is a high level of damping incorporated into the system. It is also found that the optimum tuning frequency is strongly influenced by the damping level of a system, especially in regard to the fixed‐acceleration support motion, but the optimum damping ratio of the tuned‐mass damper is not sensitive to the damping level of a system. The response of the damped system using the undamped optimum value as the damping of the tuned‐mass damper is not much different from the response using the damped optimum value.
Tsai et al. (Mon,) studied this question.