A nonlinear acoustic resonator

An acoustic resonator of Helmholtz type with a membrane attached to one of its ends is studied in this work. A membrane possesses a geometric nonlinearity of cubic type. This work examines that when attached to the resonator, a membrane can be exploited to attenuate vibrations for a variable frequency range in an acoustical system. This can be viewed as a parallel to vibration absorption for the structural systems. The coupled nonlinear mathematical model of Helmholtz resonator with a membrane attachment is investigated by applying a perturbation technique to obtain a set of second order differential equations. These equations are then numerically solved. The simulations of system frequency response show that the vibration suppression could be achieved for a wide frequency range.