Optimal Parameters of Dynamic Absorber for The Vibrations of The Beam With Moving Dynamic Absorber

Abstract

Vibration control is of utmost importance in modern mechanical and structural engineering in which excessive oscillations can cause the failure of operations, noise, fatigue, or even the collapse of the structure. Dynamic vibration absorbers provide an effective, simple and energy-efficient solution for transferring vibrational energy of the primary system to the secondary subsystem, which reduces the amplitude of the main structure. Beams are highly common structures present in bridges, vehicles, robotics, and aircraft, which exhibit complex vibrations with dynamic or moving loads, such as that of a vehicle or a crane. Consequently, a moving DVA, which moves along the beam optimizing the suppression method is required, and with parameters such as mass ratio, damping, stiffness, and position liquidating the performance of the device on such system. Although DVAs are relatively well-developed, on beams with hysteresis-type elastic dissipative characteristics, under moving loads, improper tuning of the parameters can result in reduced functionality or even increase the vibrations of the structure at certain frequencies. Consequently, this study aims at finding such optimal parameters for moving DVA on a beam and absorber with hysteresis-type elastic dissipative characteristics using purely analytical methods. As a result, the optimization allowed to reduce the amplitude and energy transmission, the parameters for which were equal to 0.1253, 1.92 and 0.5 respectively. The results were obtained through analytical modeling, resonant analysis and the Den Hartog method, were at- and transmitted power were equal to zero, are used to find the transfer function equations and the invariant points of the system under kinematic and random excitations. Numerical analysis provided optimal mass, stiffness, and damping for the moving DVA on a clamped end steel beam. The amplitude-frequency characteristic results are highlighted in that transmission is limited in the vicinity of the resonant frequencies, and the curves are shifted to the right with absorber tuning when moving and the peaks are the lowest. The work is unique in its kind as it performs such optimization using the Ginzburg method and analytical methods in order to achieve optimal suppression rather than rely on the experiment only. Results of the study can be applied to optimize values of DVAs on hysteresis beam for vibration-sensitive structures like robotic arms and high-speed railways, in order to employ maximum suppressional capabilities of the device under dynamic excitations.