Dual mode vibration isolation based on non-linear mode localization

We study a non-linear vibration isolation system capable of (a) isolating its upper part (the 'machine') from periodic disturbances generated at its base; and (b) simultaneously isolating its base from periodic disturbances generated at the level of the machine. By making use of essentially non-linear (e.g. non-linearizable) stiffness elements we completely eliminate resonances close to linearized modes, thus achieving vibration isolation over an extended frequency range. Instead, we prove the existence of branches of localized steady state motions in the frequency domain. Indeed, these localized forced motions are principally responsible for fulfilling the dual mode vibration isolation objective of this work. The method of analysis followed is based on complexification and separation of the dynamics into 'slow' varying and 'fast'-varying parts. Direct numerical simulations confirm the analytical predictions. An analytical method is then developed for determining the placement of the localized branches in the frequency domain as the system parameters vary; this permits the design of the vibration isolation system for best performance in a specified frequency range. The vibration isolation performance achieved by the non-linear system considered has no counterpart in linear theory.