Nonlinear vibration absorber design: An asymptotic approach

The one-to-one internal resonance occurring in a two-degree-of-freedom (2DOF) system composed by a damped non-linear primary structure coupled with a nonlinear vibration ab-sorber is studied via the method of multiple scales up to higher order (i.e., the first nonlinear order beyond the internal/external resonances). The periodic response predicted by the asymptotic approach is in good agreement with the numerical results ob-tained via continuation of the periodic solution of the equations of motion. The asymptotic procedure lends itself to manageable sensitivity analyses and thus to versatile optimization by which different optimal tuning criteria for the vibration absorber can possibly be found in semi-closed form.