A duct coupling system includes a first and second duct, a vibration attenuation system, a rigid ring, and a fastening system. The first duct has a first flange (314) aligned with a second flange (330) of the second duct. The vibration attenuating system abuts a first side (318) and a second side (322) of the first flange and abuts a first side (334) of the second flange. A portion of the vibration attenuating system (306) encircles the first duct. The vibration attenuating system is configured to attenuate vibrations passing between the first and second ducts. The rigid ring (302) encircles the first duct and abuts the vibration attenuation system (306). The fastening system (354) couples the first duct to the second duct and compresses the vibration attenuating system. The rigid ring does not contact the first duct and the first duct does not contact the second duct.