Issue 50

M. Godio et alii, Frattura ed Integrità Strutturale, 50 (2019) 194-208; DOI: 10.3221/IGF-ESIS.50.17 200 β=0 β=0.5 β=1 Figure 3 : Displacement history (left-hand side) and Lissajous diagrams (right-hand side) of top and bottom wall support motions with phase shift, Eqn. (8) - Nahanni record (Tab. 1). In dashed gray line: equal-amplitude sinusoidal motions shifted of 0° (top), 45° (center) and 90° (bottom). The input motions generated by the above expressions are synchronous but have unequal amplitude. Starting from Eqn. (11) it is easy to show that for any value of α, the overall support velocity is (Eqn. (1))     α u t u t    (12) and the relative velocity between the top and bottom supports is (Eqn. (2)):     α ˆu t 2αu t    (13) The factor α controls therefore the difference between the amplitude of the top and bottom support motions. As illustrated in Fig. 4, for α=0 the motion of the top and bottom supports are equal and therefore have all the same amplitude than the original input ground motion; for α=1 the bottom support is fixed and the top support moves with an amplitude that is twice the amplitude of the original input ground motion; intermediate values of α result in support motions with intermediate relative amplitude. -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2