Experimental nonlinear acoustic techniques for visualizing damage in materials and structures have been intensively developing for more than 30 years. It is of interest to supplement them by relevant modeling methods capable of imitating acoustic propagation in damaged materials. The associated gains include the availability of all calculated mechanical fields instead of restrained experimental data, the possibility to predict false detections and false alarms, and, in perspective, to reconstruct real parameters of defects by comparing measured data to synthetic ones. In this work, we model mechanical processes corresponding to laser vibrometry experiments in which nonlinear components of generated acoustic standing waves in a sample approximately reveal the position of damage. To do so, we apply a previously developed numerical method that combines a physical model of frictional contacts representing damage and the finite element formulation for acoustic waves. This physical model accounts for the Coulomb friction law governing mechanics of contacting rough surfaces by using the analogy between rough profiles and axisymmetric contacts of Cattaneo-Mindlin type. The latter ones are successfully described with the help of the original method of memory diagrams capable of calculating contact response to an arbitrary acoustic excitation. In our numerical experiments, we form standing waves in a domain containing a crack with known geometric properties. Depending on structure geometry, excitation type and strength, as well as on damage size, position and depth, we obtain widely different responses containing nonlinear spectral components. We qualitatively compare them to available experimental data and formulate conclusions on theoretical sensitivity of nonlinear resonant methods in various situations.