Systems and methods are presented for acoustic dampening in a rotating machine. The rotating machine has a rotatable shaft defining an axis of rotation and a gas flowpath. A system comprises an acoustic panel affixed to an annular casing. The acoustic panel comprises an acoustic treatment member extending between a radially inner skin and radially outer skin. The radially inner skin extends the full axial and circumferential dimensions of the acoustic panel, and the acoustic treatment member overlays the entirety of the radially inner skin. The acoustic panel is positioned so that the radially outer skin abuts the casing, the abutting surfaces being configured to effect relative axial movement between the surfaces while maintaining contact between the surfaces. The acoustic panel is affixed in position to the casing by one or more fasteners passing through the casing and a portion of the radially outer skin.