V5

First mode

Second mode

Third mode

Fourth mode

FIGURE 3.19 Normal modes. (Reprinted from Ref. [1, p. 209] by courtesy of Marcel Dekker, Inc.)

Since the beam has rotational d.o.f., Equation 3.60 becomes det(Ku) = 0, which yields fi (also l). The eigen vector {X}i is then calculated. The results are

fl

= 3.14160;

li

0 0

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