A Master of Science thesis in Mechanical Engineering by Ehab Emad Basta entitled, “Conserved-Mass Metastructures for Vibration Suppression”, submitted in April 2019. Thesis advisor is Dr. Samir Emam and thesis co-advisor is Dr. Mehdi Ghommem . Soft and hard copy available.
Vibration suppression, cancellation or absorption is an expansive field of research, which has been the focus of numerous studies performed by scientists and engineers for decades. Metamaterials are a new class of semi-active composites that can be deployed to reduce vibration of the host structure (beam) within a desired frequency. In this thesis, we investigate the nonlinear vibrations of a metamaterial structure that consists of an Euler-Bernoulli beam host attached to a periodic array of spring-mass-damper subsystems deployed for vibration absorption. The governing equations of motion of the coupled system are derived and solved numerically. A mathematical model is first utilized to perform the linear free and forced vibration analyses. The effect of the local resonators on the suppression of the oscillations of the host beam is studied. The ability to mitigate the vibration of the host structure at a desired resonant frequency is achieved by tuning the resonant frequencies of the local absorbers. More interestingly, the results show that the simultaneous suppression of several modes is possible by tuning and properly placing each absorber along the host structure. More importantly, the results show that simply adding bulk mass to the host structure barely suppresses the vibration. The comparison between metastructure and adding bulk mass confirmed that the added mass using the metastructure assembly is essentially the reason for the mitigation and not the extra mass. Furthermore, the mathematical model is used to investigate the effect of the resonators (local absorbers) on the nonlinear behavior of the main structure when being subject to external forcing over an extended frequency range. The numerical study reveals that proper tuning of the local resonators allows significant vibration suppression of the metamaterial beam when being excited in the neighborhood of any of the first three natural frequencies. We demonstrate the capability of the metamaterial structure to withstand to external loading even when operating near resonance. Finally, we combine the nonlinear mathematical model with an optimizer to identify the number and tuning frequencies of the absorbers that maximize the vibration suppression. The optimization results show that significant mitigation can be achieved by tuning properly the absorbers in the vicinity of the host structure’s natural frequencies.