Abstract Summary
The need to control and reduce the dynamic responses of a structure is strongly found. A standard technique to lower structural vibration is to use elements capable of dissipating energy. Here, the proposal to add a hysteretic element makes it possible to obtain a double result: to increase the structure dissipation characteristics and to introduce a nonlinearity which can potentially facilitate the spreading of input energy among the system vibration modes. The viscoelastic tuned mass damper (TMD) proposed by Den Hartog [1] was a great achievement in the vibration mitigation of structures; recently the beneficial effects of nonlinear devices connected to structures has been extensively demonstrated [2]. A hysteretic vibration absorber (HVA), which is described by the Bouc-Wen model, has the advantage that the restoring force combines the elastic and dissipation characteristics without the need of a damper. Moreover, its strong nonlinear characteristics activate phenomena, such as modal interactions which promotes the transfer of energy from the directly excited mode towards other modes [3]. The case of internal resonance 1:1 which resembles the Den Hartog proposal is first dealt with. Other than being a simpler solution, its effectiveness is similar to that of viscoelastic TMD, but only in a definite excitation range, due the dependence of its characteristics on the oscillation amplitude. Moreover, in this case no typical phenomena of nonlinear dynamics are activated. Different is the case of internal resonance conditions n:1, with ???? > 1 which promotes the occurrence of a rich variety of nonlinear phenomena. For the case of internal resonance 2:1, the appearance of a novel mode around the first resonance through a bifurcation mechanism involves the second mode in the response, with a beneficial effect on the vibration amplitude of the directly excited first mode. Two peaks appear in the FRC around the first resonance, for a certain value of excitation. The reduction of the response due to the HVA with respect to the uncontrolled case is evident: the picture seems similar to that of Den Hartog TMD, but instead it is completely different. A novel peak is not due to the addition of a degree of freedom, as in the case of TMD, but to an interaction with the second mode; this advantageous behaviour still remains in a large range of frequency and intensity of excitation. The case illustrated here demonstrates the efficiency of introducing a hysteretic element for the passive control of structural vibrations, but other internal resonance conditions could be advantageously investigated [1] Den Hartog, J.P. (1934) Mechanical Vibrations; McGraw-Hill: New York, NY, USA. [2] Vakakis, A.F. (2017) Intentional utilization of strong nonlinearity in structural dynamics. Proc. Eng., 199, 70–77. [3] Casini, P.; Vestroni, F. (2022) The role of the hysteretic restoring force on modal interactions in nonlinear dynamics. Int. J. Non-Linear Mech., 143, 104029.
