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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 socalled parametric antiresonance. Mechanical systems with simultaneously varying timeperiodic 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 selfexcitation 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.
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