Continuous and discrete strategies for the modal analysis of regular masonry

A modal analysis in linear elastic field for periodic masonry structures is proposed, based on continuous and discrete models. The continuum model is based on analytical homogenisation procedures, within the standard Cauchy and micropolar continuum theories, and the discrete model (DEM) describes masonry as a rigid skeleton. Both models are based on the assumptions of rigid blocks and mortar joints modelled as elastic interfaces. Modal analysis, performed with continuous and discrete models, has been carried on both at Representative Elementary Volume (REV) level and at masonry panel level, such as to evaluate masonry sensitivity to local microstructure and to characteristic length of REV compared with the masonry panel size. Hence, a parametric analysis is carried on to investigate the effect of (i) masonry texture (running versus header bond and other brick width-to-height ratios); (ii) size of heterogeneity; (iii) mortar elastic parameters; (iv) panel dimensions. Modal analysis is then carried on and compared also with a heterogeneous Finite Element Model (FEM) and a model already existent in literature (Brasile and Casciaro, 2009). The proposed modal analysis for masonry is a first step to investigate the dynamic behaviour of masonry panels. Comparisons between several models has been performed to verify the reliability of the proposed procedures and to use these different approaches for a future development in non-linear field. In addition, a modal analysis is performed to examine a full-scale masonry shear wall with constraints such as to simulate a single shear wall in a two-story masonry building, with the aim to provide a case of technical interest.