An apparatus for mounting a component in a computer includes a computer chassis and a mounting bracket assembly attached to the computer chassis. The mounting bracket assembly includes a first structural layer, a second structural layer spaced apart from the first structural layer wherein a gap is defined therebetween, and a layer of damping material disposed in at least a portion of the gap. The mounting bracket assembly is useful in space-sensitive applications while still providing vibration and acoustical noise attenuation. Furthermore, the mounting bracket assembly provides a nominal degree of impact damping during installation of a system component, reducing the potential for impact related failures.