Issue 51

M.G. Masciotta et alii, Frattura ed Integrità Strutturale, 51 (2020) 423-441; DOI: 10.3221/IGF-ESIS.51.31 435 stiffness of the springs reveal that the ordering of the mode shapes remains unchanged and the MAC values related to the first three eigenfrequencies get worse. As a second attempt a numerical simulation is performed reducing the mortar joint thickness as done in [3, 43, 44], fact that can be reasonably justified by the necessity to take into account the slight variations in thickness, corner rounding and imperfections typical of a manually assembled geometry. The results obtained by this simulation show that the only way to invert fourth and fifth mode shapes is to reduce the mortar joint thickness at least of 20%. This allows to infer that mechanical uncertainties, geometrical imperfections and block size variations do affect not only the overall capacity of an arch, but also its dynamic properties [45]. Fig. 12 shows the variation of the fourth and fifth vibration mode of the arch as a function of the mortar joint thickness. As clearly discernible in the Figure, when the thickness of the mortar joints is about 0.063 m the two frequencies coincide and the corresponding mode shapes switch. However, this modeling strategy can be exclusively adopted for the RS configuration, as it proves not to be suitable for simulating the arch dynamic behavior neither in the RSW configuration nor in the subsequent damage scenario (DS1), where the sixth experimental mode characterized by a “heart shape” disappears (or it is no longer identifiable). In addition, reducing the joint thickness causes the second and third numerical mode shapes to invert. Due to these reasons, no thickness reduction is applied to the model and only the first four corresponding modes are taken into account for the linear perturbation adopted next. Fig. 13 shows the considered experimental and numerical mode shapes for the RSW configuration; the numerical results are obtained using the parameters provided in Tab. 4 and applying to the FE model (Fig. 10) a total mass of 50 kg to simulate the lime bags symmetrically placed on the arch backs. Figure 12: Fourth and fifth mode trend vs mortar joint thickness. Tab. 6 summarizes both experimental and numerical frequencies for RSW as well as the MAC matrix between experimental and numerical mode shapes. RSW f exp f num | Δ f |[%] MAC (  exp,  num ) Mode 1 30.06 30.84 2.60 0.95 0.00 0.00 0.02 Mode 2 50.95 52.75 3.53 0.01 0.65 0.00 0.00 Mode 3 59.44 58.74 1.18 0.00 0.01 0.79 0.01 Mode 4 95.23 104.61 9.85 0.22 0.00 0.02 0.65 Table 6 : Experimental ( f exp ) versus numerical frequencies ( f num ), frequency relative error Δ f and MAC matrix for RSW.