A method and system for an acoustic panel system are provided. The system includes a plurality of acoustic panel segments aligned circumferentially about an inner diameter of a fan containment case wherein each segment includes a radially inner surface defining a portion of a fluid duct, a radially outer surface defining a gap between the fan containment case and the acoustic panel segment, and an aft end lip configured to be inserted into a mating groove in the fan containment case. The system also includes at least one damping bumper coupled to the radially outer surface wherein the bumper extends from the radially outer surface to the fan containment case and comprises an energy absorbing elastomeric material configured to facilitate dissipating a forced response of a vibratory stimulus.