Free oscillations of masonry panels and evaluation of the elasticity role

This paper deals with free oscillations of a masonry panel modelled as a unilateral (no-tension) material a la Heyman. The aim of this analysis is to evaluate the role of elasticity in the geometrically nonlinear dynamic response of structures made of such material. Two unilateral models are investigated: in the first one the material is assumed as rigid, while in the second the material is no-tension and elastic in compression. The responses of a simple panel subjected to fixed vertical compression and different initial lateral perturbations are compared, to estimate the role of elasticity for realistic values of Young’s modulus. It is shown that the time histories are periodic or quasi-periodic for rigid or elastic panels. In both cases, the oscillation periods are markedly dependent on the magnitude of the initial (rotation) data. The periodicity of elastic panels and its dependence on initial magnitude is detectable even in the purely elastic phase and is due to the physical non-linearity induced by the unilateral behaviour 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 energy distance between ‘rocking-like’ or ‘harmonic type’ models.