Parametric Studies of Frequency Response of Secondary Systems Under Ground-Acceleration Excitations
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Numerical investigation is carried out into the variation of frequency response to ground acceleration of a single-degree-of-freedom secondary system due to variations of system parameters. Selected system parameters include the mass ratio gamma between the secondary and primary systems, the running parameter beta indicating the proximity of the secondary-system frequency to a primary-system frequency, and damping of the primary system. The term "response" refers to the displacement of the secondary system relative to its support. As expected, tuning of the secondary mode to a given primary mode enhances the contributions to the total response from both modes; the highest frequency response occurs when the secondary mode is tuned to the first primary mode. Nevertheless, the first primary mode always contributes importantly even when it is not tuned to the secondary system, especially when the secondary system is heavy. When a primary mode is sufficiently detuned from the secondary system, its contribution is insensitive to the mass ratio. Increasing the damping in the primary system for the purpose of reducing the response is not very effective for heavier secondary systems. An unexpected result is found that detuning may give rise to higher response when damping is extremely low in the secondary system but is rather high in the primary system. No apparent discrepancy in the results is found whether the primary system is classically or nonclassically damped.