Optimal design of a hysteretic vibration absorber using fixed-points theory

H∞ optimum parameters of a dynamic vibration absorber (DVA) using a hysteretic or structural damping element have been derived analytically for suppressing vibration of a single degree-of-freedom (SDOF) system excited by harmonic forces or due to ground motions. Although the frequency response function of the traditional DVA (TDVA) with viscous damping may be converted to that of the hysteretic DVA (HDVA) using the equivalent viscous damping coefficient, it is found that the two frequency response functions are not equivalent after the optimization process. Therefore, the optimum parameters of the HDVA are derived using the fixed-points theory rather than converted directly from the TDVA model. The analytical results show that the optimized hysteretic vibration absorber can provide a similar vibration reduction effect as the optimized traditional dynamic vibration absorber at the resonance of a SDOF primary vibrating system. Advantages as well as the limitations of the fixed-points theory for the H∞ optimization of the hysteretic dynamic vibration absorbers using the fixed-points theory are discussed.