Closed-Form Solution to H-Infinity Optimization of Pre-Tensioned Tuned Mass Damper

Abstract

The H-infinity optimal parameters of a pre-tensioned tuned mass damper are derived to overcome the great amplitude of un-damped primary structure vibrations under harmonic excitation. In this case, damping, mass, and stiffness elements are connected directly to the ground. The two fixed points approach is used to optimize analytically frequency response function, damping ratio and pre-tensioned stiffness coefficient. The optimum pre-tensioned spring is used to keep more the stability of structure according to the principle of preload elastic device properties. Finally, the mitigation of resonance oscillation amplitude of the primary structure using the proposed dynamic absorber is compared with the traditional one. Under conditions of optimal control performance, it is proved analytically that the proposed vibration absorber with pre-tensioned stiffness provides well attenuation in the resonant vibration range. Adding, this device can be also broadening the efficient frequency range of vibration.