Abstract
Abstract The present paper proposes a new procedure to determine the optimal parameters of a dynamic vibration absorber (DVA), considering both damped and undamped primary system. The DVA design is formulated as an optimization problem in which the objective function is constructed based on Den Hartog's equal-peak method. The DVA parameters are selected to minimize the response of the primary system when it is subjected to harmonic force or base motion. Firstly, we propose a numerical strategy based on Frequency Response Curve (FRC) in which the parameters of the absorber are updated by minimizing the objective function. The results are presented for a set of reference parameters, which demonstrate the feasibility of the proposed method for determining the optimal parameters of the absorber for both excitations. Taking into account the system response with respect to reference parameters, the bilinear interpolation technique was employed in order to obtain explicit formulas of the damping and frequency ratios of the DVA.
Highlights
Dynamic vibration absorbers (DVAs) are devices used to reduce the vibration amplitudes of a primary system at certain frequencies, especially close to the resonant frequency
The optimal parameters εεoooooo and ξξoooooo has been found for each, and they are listed in Table 1 and Table 2, respectively
The investigation has been focused on the design improvement of a DVA when the primary system is subject to a harmonic or base excitation
Summary
Dynamic vibration absorbers (DVAs) are devices used to reduce the vibration amplitudes of a primary system at certain frequencies, especially close to the resonant frequency. The first design of an absorber was made by Frahm in 1909, and this first DVA did not have a damping element, only a second mass was attached to the principal one via a secondary spring This first DVA proved to be effective in a small range of frequencies very close to the natural frequency of the principal system (or called primary system). When the primary system is excited with a frequency close to natural one, the amplitudes are significantly reduced due to the presence of the DVA, if compared with the results of the primary system without the absorber In this coupled system two resonant frequencies appear one before and other after the resonant frequency of the original system. This kind of system was called a tuned mass damper (TMD)
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