On the effects of different types of nonlinearities in fast/slow dynamics of a meta-cell
Résumé
Metamaterials are systems designed to exhibit some properties which can not be found in nature [1]. One special type of metamaterials is the mass-in-mass system, which can present interesting properties such as equivalent negative mass and stiffness. The studied system, a mass-in-mass unit cell, possesses a nonlinear restoring forcing term, F(α), which depends on the relative displacement of the two masses m1 and m2 . In this work, several types of nonlinearities (unique and compound), presenting smooth or nonsmooth restoring forcing functions, are considered. System variables are complexified [2] and the resulting dynamics is treated via a time multiple scale method. It will be shown that systems with
compound nonlinearity may present some characteristics which differ from systems with classical non-linearities. Moreover, the frequency responses of the system can present isola, which should be taken into account carefully for control aspects.