Averaging in vibration suppression by parametric stiffness excitation

• Published in: Nonlinear dynamics Vol. 54; no. 3; pp. 231 - 248
• Main Authors: Dohnal, Fadi, Verhulst, Ferdinand
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2008; Springer Nature B.V
• Subjects: Actuators; Automotive Engineering; Classical Mechanics; Control; Damping; Dynamical Systems; Engineering; Excitation; Mathematical analysis; Mechanical Engineering; Original Paper; Perturbation methods; Singular perturbation; Stability; Stability analysis; Stiffness; Time integration; Vibration; Vibration control; Parametric excitation; Vibration suppression; Perturbation technique; Self-excitation; Dynamic stability
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-007-9325-z

Stability investigations of vibration suppression employing the concept of actuators with a variable stiffness are presented. Systems with an arbitrary number of degrees of freedom with linear spring- and damping-elements are considered that are subject to self-excitation as well as parametric stiffness excitation. General conditions for full vibration suppression and conditions of instability are derived analytically by applying a singular perturbation of first and second order. The analytical predictions are compared for exemplary systems by numerical time integration and show a great improvement of former results. These basic results obtained can be used for accurate design of a control strategy for actuators.