The natural frequencies of masonry beams

The present paper aims at analytically evaluating the natural frequencies of cracked slender masonry elements. The problem is dealt with in the framework of linear perturbation, and the small oscillations of the structure are studied under loaded conditions, after the equilibrium for permanent loads has been achieved. A masonry beam element made of masonry-like material is considered, and some explicit expressions of the beam's fundamental frequency as a function of the external loads and the amplitude of imposed deformations are derived. The analytical results are validated via finite-element analysis.