Enhancing the Design of Dynamic Vibration Absorbers through Harmonic Analysis and Lumped Parallel Configuration

Abstract

This work examines the utilization of negative mass and negative stiffness principles to enhance the effectiveness of Dynamic Vibration Absorbers (DVAs) for vibration attenuation developed in structures. The proposed idealized model aims to reduce the amplitude of resonance and expand the frequency stopband range to achieve vibration reduction by attaching two parallel dynamic vibration absorbers to the primary system. By incorporating stiffness, mass, and damping ratio for each one of the absorbers and in the presence of harmonic excitation, it is possible to expand the frequency range in which vibration may be suppressed, leading to a substantial decrease in the maximum vibration amplitude of the primary system and the stroke length of the absorbers. The Nelder-Mead method is successfully used as an optimization tool to obtain the best selection of the absorbers' design parameters that assure the best vibration attenuation and frequency stopband. The results indicate a strong association between the change in frequency and the decrease in vibration. In the instance of frequency response, the vibration amplitude decreased by an average of 91.46% across all three modes of the whole system. Another optimal selection exhibited the most significant enhancement, achieving an average reduction in vibration amplitude of 97.06% across all three modes. Finally, the results indicate that the suggested lumped parallel architecture of the absorbers with precisely adjusted negative mass and negative stiffness characteristics along with the presented optimization method, can greatly improve the effectiveness of reducing vibrations in various applications. The results illustrate a direct relationship between shifts in frequency and vibration. If the value of the shift is greater than 1 the vibration is decreased, while less than 1 means the worst form of reducing such magnitude. The most notable drop off in amplitude occurred when averaging a simple drop off of up to 91.46% for all three patterns where frequency shifts by Y=2.008.