36 Vibrations of Discretely Layered Structures Using a Continuous Variation Model 395 −0.5 0.5 −1 0 1 Xd 0 0.2 0.4 0.6 0.8 1 Xd 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Amplitude Amplitude Fig. 36.11 Mode shapes comparison: transfer matrix versus FDM approaches (fixed-fixed) −0.5 0.5 −1 0 1 Xd 0 0.2 0.4 0.6 0.8 1 Xd 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Amplitude Amplitude Fig. 36.12 Mode shapes comparison: transfer matrix versus FDM approaches (free-fixed) In relation to the mode shapes, comparisons for the fixed-fixed and free-fixed cases are given in Figs. 36.11 and 36.12, respectively. One can see that the FDM can produce a somewhat reasonable representation of the shapes. In order to capture the transition zone effect (seen in the transfer matrix generated modes) it is necessary to use more elements. Based on the previous results it is seen that the continuous variation model is a promising alternative to transfer matrix methods.
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