394 A.J. Mazzei and R.A. Scott −30 −20 −10 0 0 1000 2000 3000 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,1 = 2.29 wd,1 = 2.28 Fig. 36.9 First frequency via forced-motion approach (free-fixed) −5 −4 −3 −2 −1 0 1 2 3 4 −10 −20 −30 0 10 20 30 40 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 = 5.65 wd,2 = 5.64 Fig. 36.10 Second frequency via forced-motion approach (free-fixed) Table 36.1 Results comparison using transfer matrix method as baseline Transfer matrix FDM Differences (%) Forced motion Differences (%) Fixed-fixed first frequency 4.1326 3.9845 3.58 4.14 1.08 Fixed-fixed second frequency 7.3837 6.4939 12.05 7.44 0.76 Free-fixed first frequency 2.2725 1.8093 20.38 2.29 0.77 Free-fixed second frequency 5.6338 5.4604 3.08 5.65 0.25
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