Design optimization of a viscoelastic dynamic vibration absorber using a modified fixed-points theory

A viscoelastic dynamic vibration absorber (VDVA) is proposed for suppressing infrasonic vibrations of heavy structures because the traditional dynamic vibration absorber equipped with a viscous damper is not effective in suppressing low frequency vibrations. The proposed VDVA has an elastic spring and a viscoelastic damper with frequency dependent modulus and damping properties. The standard fixed-points theory cannot be applied to derive the optimum design parameters of the VDVA because both its stiffness and damping are frequency dependent. A modified fixed-points theory is therefore proposed to solve this problem. H_∞ design optimization of the proposed VDVA have been derived for the minimization of resonant vibration amplitude of a single degree-of-freedom system excited by harmonic forces or due to ground motions. The stiffness and damping of the proposed VDVA can be decoupled such that both of these two properties of the absorber can be tuned independently to their optimal values by following a specified procedure. The proposed VDVA with optimized design is tested numerically using two real commercial viscoelastic damping materials. It is found that the proposed viscoelastic absorber can provide much stronger vibration reduction effect than the conventional VDVA without the elastic spring.