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 nonoptimized 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.
Kurdi, M., Nudehi, S., and Duncan, G.S. (2016). Tailoring plate thickness of a Helmholtz resonator for improved sound attenuation. Proceedings of the ASME 2016 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE, North Carolina.