Optimization Theory Of Helmholtz Resonator And Its Experimental Validations

Medium and low frequency noise control has been one of the difficulties in the field of noise control.In this paper,Helmholtz resonators are used to solve the problem of noise control in an enclosure,which mainly develops the optimization theories of control performance of resonators and conducts experimental validations.Based on the acoustic coupling equation between resonators and the target enclsoure,damping and working bandwidth of the resonator are analyzed theoretically aiming at maximizing the reduction of the amplitude of sound pressure in the enclosure.Deduce innovatively multiple analytical solution of theory about the optimal damping ratio of the resonator,including the extreme value method,the perturbation method and the resonator source strength optimization.At the same time,analyze theoretical solutions of the three methods in detail.The optimal damping ratio obtained by the three analytical solutions is not different on the macro,which leads to the maximum amplitude of the target sound pressure.Then,the steps and methods of noise control in the enclosure with resonators are proposed.Finally,based on the one-dimensional enclosure,the above-mentioned theory is verified by experiment,and the effect of the theoretical solution applied in the low-frequency single-mode and multi-modal control is analyzed experimentally.The experimental results show that single or multiple modes in the enclosure can be well controlled with the optimization design theory of resonators when resonators are arranged at the maximum position of the mode shape.The experimental results are in good agreement with the theoretical results.Moveover,the experimental results also show that the optimal control bandwidth is proportional to the volume of the resonator,that is,the larger the resonator cavity volume is,the wider the control bandwidth is.