Free Out-of-Plane Vibrations of Masonry Walls Strengthened with Composite Materials

The natural frequencies and the out-of-plane vibration modes of one-way masonry walls strengthened with composite materials are studied. Due to the inherent nonlinear behavior of the masonry wall, the dynamic characteristics depend on the level of out-of-plane load (mechanical load or forced out-of-plane deflections) and the resulting cracking, nonlinear behavior of the mortar material, and debonding of the composite system. In order to account for the nonlinearity and the accumulation of damage, a general nonlinear dynamic model of the strengthened wall is developed. The model is mathematically decomposed into a nonlinear static analysis phase, in which the static response and the corresponding residual mechanical properties are determined, and a free vibration analysis phase, in which the dynamic characteristics are determined. The governing nonlinear differential equations of the first phase, the linear differential eigenvalue problem corresponding to the second phase, and the solution strategies are derived. Two numerical examples that examine the capabilities of the model and study the dynamic properties of the strengthened wall are presented. The model is supported and verified through comparison with a step-by-step time integration analysis, and comparison with experimental results of a full-scale strengthened wall under impulse loading. The results show that the strengthening system significantly affects the natural frequencies of the wall, modifies its modes of vibration, and restrains the deterioration of the dynamic properties with the increase of load. The quantification of these effects contributes to the understanding of the performance of damaged strengthened walls under dynamic and seismic loads.