Vibrations of Elastic Systems by Edward B. Magrab

Vibrations of Elastic Systems by Edward B. Magrab

Author:Edward B. Magrab
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht


(3.382)

When , Ω n are the solutions to and, from Case 8 of Table 3.3, the mode shape is

(3.383)

From Eq. (3.373), the norm is

(3.384)

After some numerical experimentation, it is found that good convergence of Eq. (3.379) is obtained by using the lowest 10 natural frequencies and their corresponding mode shapes. The results are shown in Figs. 3.47 and 3.48. In both figures, the parameters are and 100, and and 0.4. In Fig. 3.47, the load is applied at and in Fig. 3.48, at . The duration of the non dimensional time τ that is displayed is chosen as the period τ 1 of the lowest natural frequency; that is, . This time varies with the presence or absence of K i and m R and is given for each case.

Fig. 3.47Impulse response of a cantilever beam with and without a mass at its free end and without an in-span spring when the impulse force is applied at (a) (b) (c) (d) . The quantity τ 1 is the non dimensional period of the lowest natural frequency



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