This work is motivated to determinate the optimal design for various types of Dynamic Vibration Absorbers (DVAs) under the effect of random loads. These devices are the following: DVAs connected in parallel or series; two degree-of-freedom traditional dynamic vibration absorber (2dof-TVA) with translational and rotational motion; and inerter-based DVAs (IDVA-C6, C4, and C3). These types of DVAs were selected by their high effectiveness for suppressing vibration however a comparative study on their dynamic performance has not yet been performed. Two different excitation sources of random loads are studied in this paper which are random ground motion and force excitation. An optimum design for majority of these devices has not yet been computed when subjected to random ground motion excitation, and therefore in this paper are computed. For random force excitation, some numerical solutions for the optimal design of these devices have not yet reported which in this paper are computed in order to compare the dynamic performance for each device with respect to that of the classic DVA. For both random excitation cases, the H2 optimization criteria is used to analytically compute the variance of squared modulus of frequency response of the undamped primary structure, and then nonlinear unconstrained optimization problems are formulated in order to obtain the optimal design. Numerical solutions revealed that the IDVA-C6, C3, and DVAs connected in series presents more than 13% and 10% improvement with respect to the classic DVA for random ground motion and force excitation cases, respectively. These devices can widen the suppression band (SB) from 30% to 40% for mass ratios values from 1% to 10%. It means that devices are more effective and robust for mitigating vibration than the classic DVA. In addition, the rotational inertial double tuned mass damper (IDVA-C6) has the same relative dynamic performance (RDP) and suppression band index (SB) than the double-mass dynamic vibration absorber arranged in series. For practical application where the mounting space of the DVA is extremely reduced, the DVAs connected in series could be more convenient to use than IDVA-C6. The concept of equivalent mass ratio is introduced in order to explain the superiority of these devices with respect to the classic DVA. Finally, in H optimization criteria, the IDVA-C6 presents the same vibration amplitudes at all excitation frequency range and suppression band than DVAs connected in series.

Introduction

During the last decades, various types of mechanical devices have been proposed for the passive vibration control in civil engineering. These devices are known as the dynamic vibration absorbers (DVAs) or tuned mass dampers (TMDs) [1]. The main target of a DVA is to mitigate the dynamic response of mechanical structures under the effect of earthquakes, wind, maritime waves excitation, unbalanced rotating machinery, and dynamic vibration caused from vehicle traffic. In recent studies, the performance of the classic DVA has been enhanced by means of different connections of energy dissipation (dashpot) and absorption (spring) elements of the absorber, which the classic DVA is re-named as the non-traditional DVA, and Three-Element DVA [2–۵]. In addition, different researches have been performed on the dynamic behavior of classic DVAs to improve the frequency response of the main structure when subjected to various types of excitation sources [6–۱۰]. Additionally, Krenk and Høgsberg introduced a classic DVA on a flexible structure to provide damping on a specific vibration mode, and thus reduce the dynamic magnification factor (DMF) of main structure [11]. They noted that the background flexibility of the main structure leads to higher design values for the absorber frequency and damping parameter. However, these improved DVAs only minimize the dynamic amplification factor of frequency response, but they do not improve the effective operating bandwidth or suppression band.