Page 576 - Aircraft Stuctures for Engineering Student

13.3 Structural vibration 557

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Fig. 13.1 1 The second natural mode of the massheam system of Fig. 13.9.

Example 13.2
Find the lowest natural frequency of the weightless beam/mass system shown in
Fig. 13.12. For the beam GJ = (2/3)EI.

The equations of motion are
mij1611 + 4WZW261~ + w1 = 0 (i 1
mv1621 + 4mv2622 + v2 = 0 (ii)

In this problem displacements are caused by bending and torsion so that

(iii)
From Fig. 13.12 we see that

M1= lx O<X<l
M1 = l(21- z) 0 < z < 21
M2=1(1-z) O<Z<l
M2 =o I<z<21, O<X<l
TI = 11 O<Z<21

Ti =O O<X<l
T2 = 0 0<-7<21, O<X<l

Fig. 13.1 2 Massheam system for Example 13.2.