In this paper, a random sampling scheme based on Compressive Sensing (CS) is used in order to reduce the acquisition time of wavefield signals by means of a scanning laser Doppler vibrometer (SLDV) for Structural Health Monitoring (SHM) applications. The sampling process is indeed quite time consuming, because of noise sources and reduced amplitude of acquired signals. By virtue of the sparse characteristic of the wavefield signal representation in terms of sparsity-promoting dictionaries, e.g. Fourier, Curvelet and Wave Atom transforms, the signal can be however recovered through a limited number of measurements. The implemented CS-based procedure has been validated with experimental signals sub-sampled in a pattern of random distributed points, demonstrating the effectiveness of the approach to limit the acquisition time with extremely low information losses.