On the role of elasticity in the dynamics of unilateral structures. The case of free oscillation of a masonry panel

In this paper we analyze the free oscillations of a masonry panel made of unilateral no-tension material, essentially assuming the model proposed by Jacques Heyman. The aim of this analysis is to evaluate the role of compressive elasticity in the geometrically nonlinear dynamic response of masonry structures. Therefore, two models are considered: the first assumes that the material is rigid, while the second one that the material is unilateral (No-Tension) and elastic in compression. Different levels of realistic values of Young's modulus, and the responses of a simple panel subjected to fixed vertical compression and different initial lateral perturbations are compared, to estimate the role of the elasticity. As the time histories of rigid and elastic panels show, the response of the rigid block is periodic, while that of the elastic No-Tension block is quasi-periodic. In both cases, the oscillation periods are visibly dependent on the amplitude. The periodicity of elastic panels and its dependence on amplitude is detectable even in the purely elastic phase and is due to the physical non-linearity induced by the one-sided restrictions of the material. The comparison between rigid and elastic time histories shows the main differences between rigid and elastic cases and allows to quantify the accuracy of the "rocking-like" hypothesis compared to the "harmonic type" simplification.