Abstract
In this paper, we study the dynamics of a two-degree freedom system consisting of the main body and tuned mass damper with inerter (TMDI). We add the dash-pot with variable damping coefficient to TMDI to study the overall efficiency of the device. We investigate different types of the non-linear characteristic of the dash-pot. We investigate devices in which damping coefficient change according to the relative displacement or the relative velocity between the damped mass and tuned mass damper. We also include in the investigation of different types of control functions. We show the two-parameter diagrams presenting the main body’s maximum amplitude versus the frequency of excitation of the damped body and different control parameter. We show how the application of a non-linear damper lets us control the main system’s oscillation amplitude.
Highlights
Vibrations of machines and structures under external excitation are usually unwanted
We investigate 8 different functions that describe changes in damping coefficient based on the displacement or velocity of the tuned mass damper
For a low value of a, we observe two resonances and for the maximum value of a, the main mass and tuned mass damper with inerter (TMDI) behave like one DoF system
Summary
Vibrations of machines and structures under external excitation are usually unwanted. The span of frequency where we observe a significant decrease in the amplitude dependents on damping coefficient of the TMD dash-pot. When it is equal to zero, the amplitude of the main body drops down to zero for resonant frequency, but TMD is effective in the very narrow frequency range close to the resonance. The increase in damping coefficient increases the effective range of mitigation of oscillations, but the amplitude of the main body is no longer zero in the resonance. Den Hartog [2] proposed a method to calculate the optimum value of damping coefficient of the TMD dash-pot. Even in the optimized case, we still observe a significant increase in the main body oscillations amplitude around the resonance frequency
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