The more fringes on a blade, the higher the vibration amplitude for that blade. In the mode shape images, vibration is indicated by dark fringes, with each fringe corresponding to a certain level of vibration. Normal modes of a bladed disk, measured experimentally using electronic speckle pattern interferometry. Other illustrations of mode localization are shown in Figures 8 and 9, for a multispan beam on randomly spaced supports and a two-dimensional multipanel membrane resting on randomly spaced elastic line supports, respectively.įigure 11. Note that energy confinement also results in larger amplitudes (both modes were normalized by the same energy). While the mode of the ordered assembly extends through the structure, the corresponding mode for the disordered assembly is localized about a few beams. The standard deviation of disorder is on the order of typical manufacturing tolerances and the inter-beam coupling stiffness is significant.
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Figure 7 displays typical free vibration modes for an ordered assembly of 100 identical beams and a slightly disordered system. To illustrate such strong localization, consider the monocoupled assembly of component beams in Figure 6. Under conditions of weak coupling between bays or, equivalently, high modal density, the effects of small disorder can be drastic.
The degree of localization in a structure depends on the ratio of disorder strength to internal coupling strength and increases with this ratio.