Page 278 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 8 Problems 265

8-15 Using matrix iteration, determine the three natural frequencies and modes for the
cantilever beam of Fig. P8-15. Note: The flexibility matrix in Example 6.1-3 is for
coordinates given in reverse order to above problem. They can be rearranged for
above problem which requires the inverse if the computer program ITERATE is to be
used.

(1) (2) (3)
- O ^ hC ^ ^ - O
m m m Figure P8.15.

8-16 Using matrix iteration, determine the natural frequencies and mode shapes of the
torsional system of Fig. P8-16.

Figure P8.16.

8-17 In Fig. P8-17 four masses are strung along strings of equal lengths. Assuming the
tension to be constant, determine the natural frequencies and mode shapes by matrix
iteration.

/ £ Figure P8.17.

8-18 Decompose the stiffness matrix K = U^U for Fig. P8-18.
/ r - 2 - 1
-1 4

^ /c 3/f ^
'^y-N\N\r- - A M A r- -VyA/V-^
i
Figure P8.18.

8-19 Repeat Prob. 8-18 for the system shown in Fig. P8-19.
3 - 1
-1 1

I 2*
|-AAAAt- -N\N\r-
^2 Figure P8.19.