Attenuation of an acoustical mode by using an Helmholtz resonator with nonlinear behavior

We show that it is possible to use nonlinear resonator to attenuate very low frequencies for which the classical porous materials are less efficient in a vehicle. The mass or the thickness of the porous material must be big to achieve this goal. Modified geometry of the neck of the Helmholtz resonator (HR) is considered to decrease the damping and activate cubic nonlinearities of the pure acoustical resonator for high levels of amplitude. For the HR, nonlinear restoring and damping forces are taken into account. By activating cubic nonlinearity, it is possible to obtain targeted energy transfer from one acoustical mode to an HR with nonlinear behavior. To design the system, analytical developments are performed. A time multiple scale method associated with a complexification method are used for detection of different system dynamics. Strong modulated responses of the system can be obtained to decrease the level of energy. Analytical predictions are compared with those which are obtained by direct numerical integration of system equations. Experimental verifications are performed and presented. It is shown that attenuation of large amplitudes is accelerated and that the nonlinear resonator allows to broadband the frequency range where the system is efficient.