Damping of Mechanical Vibrations by Parametric Excitation

The goal of this work is to develop deeper insight

into the method of damping vibrations by means of

parametric excitation in mechanical systems ¿

employing the concept of the so-called parametric

anti-resonance. Mechanical systems with

simultaneously varying time-periodic stiffness,

damping and inertia coefficients are examined. At

least two vibration modes are necessary to achieve

damping. For these minimum systems a thorough

stability analysis is carried out using a

perturbation technique.

Parametric excitation may lead to a coupling of just

two modes of a vibrating system, while the remaining

modes are not affected. This coupling enables to

transfer energy between modes and its subsequent

mitigation. The results demonstrate that parametric

excitation can be employed to extend significantly

the area of stability in the parameter space of the

system parameters. The proposed method shows

potential in practical applications when a

destabilization due to self-excitation occurs or when

the damping of weakly damped systems shall be

enhanced. The present book can be used as a

comprehensive guide for designing a device for

vibration suppression by parametric excitation.