Conception et évaluation des performances de quelques systèmes passifs de suppression de vibrations à base d’inerter avec ou sans rigidité négative.

Abstract

This thesis proposes some mechanical inerter-based networks C1, C2, C3, C4, C5, C6 and C7 in series or series-parallel arrangement with or without negative stiffness for passive vibration control of an undamped single-degree-of-freedom primary structure under base excitation or force excitation directly applied to the primary mass. The necessary and sufficient conditions to guarantee the stability of the C4, C6 and C7 devices with negative stiffness are established according to the Routh-Hurwitz criterion and the stability boundary is obtained. The parameters for setting the proposed C1, C2, C3, C4, C5, C6 and C7 devices are determined under harmonic excitation by the fixed points theory based on the H∞ optimization and the H2 optimization in case of random excitation. A comparison between the performance of the proposed devices in this study an conventional TMD (or TDVA) and TID dampers is presented in terms of : (1) reducing the peak vibration amplitude of the primary mass for the cases of harmonic, transient and random excitations (white noise), respectively, (2) the vibration suppression bandwidth considering harmonic excitation, (3) the stabilization of the primary structure in the event of transient excitation and (4) reduction of the noise generated by the primary structure in the random excitation (white noise). The results of this study demonstrated that under harmonic excitation of the base of the primary system, the proposed C1, C2, C3, C4 devices exceed TMD (or TDVA), respectively, in terms of suppression bandwidth more wide and the reduction of the maximum amplitude of the primary mass significantly. Meanwhile, in the case of random excitation, these devices also outperformed TMD (or TDVA) , respectively, in terms of reduction of the root mean square response and the time history of the primary structure. In addition, the proposed C1 and C2 device contributed to reduce the noise generated by the structure under harmonic and random excitation of the base of the primary structure in comparison with the TDVA. In the case of harmonic force excitation of the primary structure, C5, C6 and C7 each surpassed the TID, respectively, in terms of suppression bandwidth more wide and reduction of the maximum amplitude of the primary mass significantly, with a smaller installation space (stroke lenght). Meanwhile, C7 with grounded negative stiffness coupled with an inertance amplification mechanism presented three boxes of figure on the value of the grounded stiffness ratio according to the change in amplification ratio, i.e. negative, zero and positive. Finally, the further comparison among these devices C5, C6 and C7 and TID under white noise excitation also shows that C7 is superior to the others for a given mass ratio. Theoretically the C7 configuration with grounded positive stiffness has the best control performance than the other two cases and in the comparison with the devices of C5, C6 and TID. Finally, the free vibration response of the primary system under transient excitation was evaluated with the devices C3, C4 and TMD, while that under sinusoidal excitation was evaluated with the devices C5, C6, C7 and TID, and comparisons have been given. In both cases on evoked, the devices C3, C4, C5, C6 and C7 compared to TMD and TID, respectively, showed better control performance characterized by the smallest amplitude of the primary system response and a stabilization time more cost in the case of transient excitation in particular. However, for the two mentioned above cases, the devices C4, C6 and C7 with negative grounded stiffness have once again again showed remarkable control performance compared to C3, C5 devices without negative stiffness, while C7 in its case 3 with positive grounded stiffness is superior to all other devices. Finally, devices with negative grounded stiffness showed superiority over compared to those of devices without negative stiffness. Thus, the complexity of the negative stiffness system is also a factor to be considered in actual engineering. However, obtaining negative stiffness is difficult in engineering practice. Therefore, the device C7 in its case 3 with positive grounding stiffness, which showed much superior performance compared to devices Ci (i = 1,2, .., 6) with or without negative stiffness, deserves special attention in this thesis. This result could provide a theoretical basis for the design of inerter-base isolators or absorbers with or without negative stiffness.