A shim structure is provided for damping vibration and attenuating noise in a brake system. The brake system includes a forcing member operable to urge a friction member against a rotating member to slow or stop the same. The shim structure includes a shim body that is adapted to be interposed within the brake system. The shim body includes one or more tabs that are configured to oscillate out-of-phase with vibrations generated by the brake system during urging of the friction member against the rotating member to thereby dissipate vibrational energy generated by the brake system. The dimensions, orientation, and/or location of each tab are selected or engineered to provide predetermined levels of vibration and noise attenuation. A mass may be attached to each tab. The geometry, location, and/or size of each mass may be selectively modified to provide predetermined levels of vibration and noise attenuation.