Optimizations of dynamic vibration absorbers for suppressing vibrations in structures

Hinfinity and H2 optimization of the traditional dynamic vibration absorber (DVA) in single degree-of-freedom (SDOF) system are classical optimization problems and have been already solved for a long time. However, the Hinfinity and H2 optimization of the dynamic vibration absorbers in multi-degree-of-freedom (MDOF) or continuous systems have not been solved. Some researchers found out the optimum tuning conditions of MDOF or continuous systems but all the methods found in the literature are numerical optimizations and the results cannot provide physics insight on the effect of each tuning parameter to the performance of vibration suppression of the primary vibrating system. Optimization theories of the traditional DVA for suppressing vibration in beam and plate structures have been established and reported in this thesis, and better tuning conditions of the DVA have been found in comparison to those reported by other researchers.Non-traditional designs of the DVA are some recent research topics. One of these designs has been proved to perform better than the traditional design in some applications and it is studied and reported in this thesis. Researchers in this area tend to use the fixed-points theory of Den Hartog (1985) in searching the optimum tuning conditions of DVAs. However, it has been shown in this thesis that the fixed-points theory may not applicable in some tuning conditions of a non-traditional DVA. A new theory is established for finding the optimum tuning condition of the non-traditional DVA.