36 Vibrations of Discretely Layered Structures Using a Continuous Variation Model 393 0 25 20 15 10 5 0 Xd 0 0.2 0.4 0.6 0.8 1 Xd 0 0.2 0.4 0.6 0.8 1 −10 −20 Rod deflection Rod deflection −30 wd,1 = 4.14 wd,1 = 4.13 Fig. 36.7 First frequency via forced-motion approach (fixed-fixed) −0.04 −0.02 0.02 0.04 0.06 0.20 0.15 0.10 0.05 −0.05 0 0 Xd 0 0.2 0.4 0.6 0.8 1 Xd 0 0.2 0.4 0.6 0.8 1 Rod deflection Rod deflection wd,2 = 7.44 wd,2 = 7.43 Fig. 36.8 Second frequency via forced-motion approach (fixed-fixed) 36.5 Comparisons In the following the results produced by the numerical approaches utilized above are compared to the values obtained using the transfer matrix method. These are summarized in Table 36.1. Note that the forced-motion approach produces very accurate results when compared to the transfer matrix method. It can be utilized with confidence as an alternate method when the matrix approach becomes mathematically complex. The FDM produces reasonable results.
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