Crossing phenomena is present for k2-3 = 100% kBar (Figure 7 on the left), in fact this value allows the model to possess axial-symmetric property and then to have coincident eigenvalues. In case of different stiffness, i.e. k2-3 = 100% kBar, curve veering appears in some couples of modes (Figure 7 on the right). When it is imposed a stiffness parameter variation, different by a circumferential variable parameter like k2-3, it will be obtained a curve veering phenomena. When symmetric characteristics are not present, most of crossing phenomena involving mode-shapes of Figure 6 became veering, but some curve crossing between bending and torsional modes are still evident. In Figure 7 letter “C” and ellipse specify curve crossing point, whilst letter “V” and rectangle specify curve veering point. Similarly, to order eigenfrequencies a swap matrix obtained from MAC across every point of veering and/or crossing phenomena is adopted. Figure 5 – Bell and corresponding FE model. -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 MODE 4 - Freq = 685.23 Hz x axis [m] y axis [m] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 MODE 5 - Freq = 685.23 Hz x axis [m] y axis [m] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 MODE 6 - Freq = 702.53 Hz x axis [m] y axis [m] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 MODE 7 - Freq = 702.53 Hz x axis [m] y axis [m] Figure 6 – First mode-shapes of the bell system (red lines) superimposed on the underformed shapes(blue lines). 330
RkJQdWJsaXNoZXIy MTMzNzEzMQ==