Metallic materials such as brass, copper, and aluminum are used in numerous applications, including industrial manufacturing. The vibration characteristics of these objects are unique and can be used to identify these objects from a distance. This research presents a methodology for detecting and classifying these metallic objects using the vibration dynamics induced by their micro-Doppler signatures. The proposed approach utilizes image processing techniques to extract pivotal features from spectrograms. These spectrograms originate from micro-Doppler signatures of data collected during controlled laboratory experiments where signals were transmitted towards vibrating metal sheets, and the ensuing reflections were recorded using a software-defined radio (SDR). The spectrogram data was augmented using geometric transformation to train a convolutional neural network (CNN) based machine learning model for object classification. The results indicate that the proposed CNN model achieved an accuracy of more than 95% in classifying metals into brass, copper, and aluminum. This research could be used to understand the foundations of classifying spectrogram images using micro-Doppler signatures for its applications towards enhancing the sensing capabilities in industrial and defense applications.