Targeted energy transfer from one acoustical mode to a Helmholtz resonator (HR) with nonlinear behaviors is studied. For the HR, nonlinear restoring forces and nonlinear damping are taken into account. A time multiple scale method around a 1:1 resonance is used to detect slow invariant manifold (SIM) of the system, its equilibrium and singular points. Analytical predictions are compared with those which are obtained by direct numerical integration of system equations. Experimental verifications are performed and presented for free and forced vibrating system.

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