Identification of equivalent mechanical properties for unreinforced masonry walls

Transverse vibrations of beams are an interesting topic for numerous engineering fields. The equations of motion develop under various assumptions and associate a frequency equation. This paper expresses the frequency equation for two specific models, using the Timoshenko beam theory. The first model is a typical cantilever beam with an additional mass attached to the free end. The second model considers a beam partially clamped at the base and with an elastic connection of the additional mass to the free end. The relevance of the used theory is discussed and the importance of each term of the equation is studied. These models find applications in unreinforced masonry. They are indeed fitted to identify, from white noise tests, equivalent mechanical properties of unreinforced load-bearing clay masonry walls including soundproofing devices in the perspective of modelling these elements with a macro-scale approach. Discrepancies with respect to current standards are underscored.