The work is focused in investigating the effectiveness of discretized damping tapes applied to a cantilever beam subjected to free and forced vibrations. The work is divided into three main sections. First, we performed material characterization of the viscoelastic (VE) pressure sensitive adhesive layer of the damping tapes. To do so, we designed a novel quad shear specimen to measure shear storage and loss moduli, and tan delta from dynamic mechanical analyzer measurements. Second, the optimal discretization length for different damping tapes was experimentally determined and analytically verified using linear viscoelasticity and basic strength of materials and vibrations principles. These results showed a mean to improve the damping of a structure without increasing the weight of the added damping layer. Third, a nonlinear analysis was performed for cantilever beams with damping layers subjected to parametric excitation. Comparison of the response amplitude of the parametrically excited beam was performed for different discretization lengths, and system identification of the nonlinear parameters was carried out. The effects of large deflections of a beam under parametric excitation were analyzed; large deflections were found to induce localized buckling of the stiff constraining layer of the damping tape that would invalidate some of the assumptions and analytical solutions that do not take such phenomena into account. / Master of Science