Damping is an effective way of suppressing mechanical vibrations. Passive layer damping patches are often used in the industry as damping solution for vibrations and acoustics problems. In this study, topology optimization methods were applied to the finite element models (FEM) of plates and damping patches in order to determine the critical locations for the frequency range of interest. Correlation of the finite element model with experimental data is performed both on modal analysis and frequency response functions. The optimized damping patch topology is compared to the base plate with full application of damping patch on frequency response functions. Finally, the thickness of the damping pads is varied to see its effect on the frequency response functions.