Page 211 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

198 Properties of Vibrating Systems Chap. 6

¡ 1 'c • ~ ~T ' 1 ’

(a)

Thus, the roots or the eigenvalues for the system are
Ai = 0
A2 = 1

To identify the corresponding eigenvectors, each of the A’s is substituted into
the equation of motion:
(1-A ) - 1 0
0 (2 -A ) -1
0 -1 (1-A )
When Aj = 0 is substituted, the result is = ^2 ^ ^3 normal mode, or
eigenvector, is
*, = |!

which describes the rigid body motion [see Fig. 6.12-2(a)].
Similarly, the second and third modes [see Figs. 6.12-2(b) and 6.12-2(c), respec­
tively] are found and displayed as
n ( 1
(t>2 '■= 0 <^3 = - 2
1 1

P R O B LEM S

6-1 Determine the flexibility matrix for the spring-mass system shown in Fig. P6-1.

«1 3 ^

V7777777//, Figure P6-1.