A multi-objective optimization formulation to design a Helmholtz resonator with a flexible end plate is studied. The optimization formulation generates a Pareto curve of design solutions that quantify the trade-off between the optimization goals: minimum resonator volume and maximum transmission loss across a specified frequency range. The optimization problem is formulated and solved in the following manner. First, a mathematical formulation for the transmission loss of the Helmholtz resonator with a flexible plate is completed based on the design parameters. Then, the weighted transmission loss across a specified frequency range and a minimum resonator volume are defined as optimization objectives. Finally, the Pareto curve of optimum design solutions is calculated using a gradient-based approach via the ε-constraint method. The optimization results allow the designer to select resonator design parameters that meet the requirements for both transmission loss and resonator volume. To validate the optimization results, one optimal Helmholtz resonator is manufactured and experimentally confirmed.

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