In this growing world, it is imperative to employ innovative techniques that effectively manage the structural response of materials without inducing adverse effects on the original structure. This can be achieved mainly by changing the material and geometrical features of the adhesive. In this work, an attempt has been made to control the eigenvalues of adhesively bonded single-lap joints (SLJs) by reinforcing them with polymer patches. Numerical techniques were utilized to adhere the polymer patches to the single-lap bonded joints using ABAQUS software. Subsequently, the eigenvalue responses of SLJs, both with and without patches, were experimentally well agreed with the numerical predictions. The validated numerical model was then used to investigate its structural response by modifying the parameters such as patch shape, patch position, and adhesive geometry. Additionally, it has been observed that a square-shaped polymer patch at the overlapping edge is more effective in reducing the eigenvalues compared to patches of different shapes and positions. The eigenvalue response follows a declining trend as the adhesive thickness increases, forming thicker bonds.