The presence of damage significantly affects the system’s performance. Various damage detection methods are available to identify damage in engineering structures. The guided wave propagation-based nondestructive evaluation (NDE) methods have proven their potential to effectively identify damage in such advanced structures due to the long-distance inspection capability and the capacity to interrogate the whole thickness of a structure. Therefore, in the present study, the laser Doppler vibrometer (LDV) and numerical simulations are used to study the guided wave propagation and their capabilities to identify different types of damage regions in a sandwich-like structure comprising of an aramid core and aluminum skin. The piezoelectric sensor-based excitation is used. The damage involved in this study is barely visible impact damage (BVID) of different diameters and a hole. The presence of damages causes abrupt changes to the wave field of the guided waves. Full field and elliptical-based signal processing methods are used in determining the region of damage. Thus, the damage region is visualized in this comparative study.