Control of sound transmission through double wall partitions using optimally tuned Helmholtz resonators

An arrangement of Helmholtz resonators (HRs) used for the passive control of sound transmission through a double wall partition is investigated. By using the modal expansion method, the partitions walls, acoustic cavity field as well as Helmholtz resonators are described by a set of partial differential equations, leading to a full analytical model. The Helmholtz resonator sound transmission control mechanism is based on adding damping to the acoustical resonances of the cavity inside the double wall partitions. Firstly, a method to compute optimal damping ratios for the whole arrangement of Helmholtz resonators guaranteed broadband improvement of sound isolation is presented. Secondly, due to the strong coupling between the cavity acoustic modes and structural modes of the partition walls around the mass-air-mass resonance frequency, tuning the Helmholtz resonators exact to the mass-air-mass resonance frequency cannot guarantee improvement on transmission loss. Optimal natural frequencies of Helmholtz resonators were found as a solution of optimization problem with a global cost function defined as frequency averaged sound transmission loss in the desired frequency range (around mass-air-mass resonance frequency). Finally, some simulation results are presented. The simulation results confirm that using optimally tuned arrangement of Helmholtz resonators the sound transmission loss of a double wall partitions can be improved significantly in the desired frequency range. In presented case an overall improvement 8 dB in the 50 - 150 Hz band is obtained by using I resonator (requiring only 2.8% of the double plate cavity volume), and a 10 dB improvement obtained by using 3 resonators (requiring 8.4% of cavity volume).