A Helmholtz resonator with flexible plate attenuates noise in exhaust ducts, and the transmission loss function quantifies the amount of filtered noise at a desired frequency. In this work the transmission loss is maximized (optimized) by allowing the resonator end plate thickness to vary for two cases: 1) a non-optimized baseline resonator, and 2) a resonator with a uniform flexible endplate that was previously optimized for transmission loss and resonator size. To accomplish this, receptance coupling techniques were used to couple a finite element model of a varying thickness resonator end plate to a mass-spring-damper model of the vibrating air mass in the resonator. Sequential quadratic programming was employed to complete a gradient based optimization search. By allowing the end plate thickness to vary, the transmission loss of the non-optimized baseline resonator was improved significantly, 28 percent. However, the transmission loss of the previously optimized resonator for transmission loss and resonator size showed minimal improvement.

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