Laser-scanning-based damage-detection techniques have been employed for various structures. Although they are effective for simple structures, they exhibit poor performance for complex-shaped structures owing to their thickness variations and numerous boundary conditions. Therefore, this paper presents a baseline-referenced damage-detection method that visualizes damage by analyzing the differences between the wavenumbers of healthy structures and those with structural damage. The steady-state response generated through a single-frequency excitation was measured through laser doppler vibrometry scanning and divided into local regions. Subsequently, damage indicators were extracted through directional comparisons in the wavenumber domain and the damage was visualized by mapping them to local spatial regions. The proposed technique was validated through experiments on both aluminum plates with reinforced ribs and composite plates. The results indicated that the proposed method can accurately detect the location and extent of damage in complex structures. Additionally, it effectively distinguishes between the wavenumber changes caused by the structural geometry and those caused by damage, thereby enabling accurate damage detection for complex structures where the use of conventional methods is challenging.