The systems and methods described herein relate to a dome of a gas turbine assembly configured to suppress pressure pulsations. The systems and methods provide a dome having an aperture configured to surround an injector assembly of a combustor. The dome having a front panel extending radially from the aperture. The systems and methods couple a first cavity to the front panel. The first cavity includes a series of ducts. A first duct of the series of ducts is configured to receive airflow into the first cavity from a compressor and a second set of ducts of the series of ducts and a third duct of the series of ducts are configured to direct airflow to the combustor from the first cavity, wherein the third duct has a larger diameter than the second set of ducts.