Application of nonlinear localization to the optimization of a vibration isolation system

We consider a passive nonlinear mechanical vibration isolator consisting of discrete mass, stiffness, and damping elements. We show that, by suitably designing the stiffness nonlinearities, we can induce localized nonlinear normal modes (NNMs) in this system. These are unforced oscillations analogous to the normal modes of classical linear vibration theory, with energies that are spatially confined. When the isolator with localized NNMs is subjected to harmonic excitations in certain frequency ranges, the resulting resonances become similarly localized and the level of the transmitted undesirable vibrations is greatly reduced. Hence, nonlinear localization can provide a valuable tool for developing improved vibration and shock isolation designs, otherwise unattainable using linear theory. In addition, we develop a technique that systematically optimizes the localized NNMs of the unforced isolator, by localizing the vibrational energy in a way that is compatible to the vibration isolation objectives. This ensures minimal transfer of unwanted disturbances when a harmonic excitation is applied to the system.