**Beata Zima \* and Rafał K ˛edra**

Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gda ´nsk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland; rafal.kedra@pg.edu.pl

**\*** Correspondence: beata.zima@pg.edu.pl

Received: 6 May 2020; Accepted: 3 June 2020; Published: 4 June 2020

**Abstract:** The article presents the results of the numerical investigation of Lamb wave propagation in concrete plates while taking into account the complex concrete mesostructure. Several concrete models with randomly distributed aggregates were generated with the use of the Monte Carlo method. The influence of aggregate ratio and particle size on dispersion curves representing Lamb wave modes was analyzed. The results obtained for heterogeneous concrete models were compared with theoretical results for homogeneous concrete characterized by the averaged macroscopic material parameters. The analysis indicated that not only do the averaged material parameters influence the dispersion solution, but also the amount and size of aggregate particles. The study shows that Lamb waves propagate with different velocities in homogeneous and heterogeneous models and the difference increases with aggregate ratio and particle size, which is a particularly important observation for wave-based diagnostic methods devoted to concrete structures.

**Keywords:** concrete; mesostructure; Lamb wave; heterogeneity; Monte Carlo method; SHM
