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.