Page 277 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

264 Computational Methods Chap. 8
becomes

(/Cj + /C2) (/C2/2 - ^1^1) 1 -*2
J I
----y e ) -f (^2^2 ^ ^1^1) (*,/? + *2/|) A:,/, - * 2/2 d

mo < -{0}

- k . A,/, 1*0 + *1 0
mo - k 2 “ ^2^2 1 0 k „ + *2
Draw the spring-mass diagram for the configuration and derive the foregoing equation.
8-12 Additional data for Prob. 8-11 are Wg = mQg = 160 lb and /cq = 38,400 Ib/ft. Using a
computer, determine the four natural frequencies and mode shapes, compare with the
results of Example 5.3-2, and comment on the two.
8-13 The uniform beam of Fig. P8-13 is free to vibrate in the plane shown and has two
Wn
concentrated masses, mj = — = 500 kg and m2 = — ^ 100 kg. Using the iteration
method, determine the two natural frequencies and mode shapes. The flexibility
influence coefficients for the problem are given as
_ P _ P
48£/ 6^22’ "22 8£;/.
P 1
i7i9 — — ^22

Figure P8.13.

8-14 Determine the influence coefficients for the three-mass system of Fig. P8-14 and
calculate the principal modes by matrix iteration.

^3 Figure P8.14.