Page 289 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

276 Vibration of Continuous Systems Chap. 9

Example 9.3-3
Using the frequency equation developed in the previous example, determine the first
two natural frequencies of an oil-well drill pipe 500 ft long, fixed at the upper end and
terminating at the lower end to a drill collar 120 ft long. The average values for the
drill pipe and drill collar are given as

Drill pipe: outside diameter = 4^ in.
inside diameter = 3.83 in.
//, = 0.00094 ft^ / = 5000 ft
490
Jrod = Ippl = 0.00094 X X 5000 = 71.4 lb • ft • s"

Drill collar: outside diameter = 7 | in.
inside diameter = 2.0 in.
= 0.244 X 120 ft - 29.3 lb • ft • s"

Solution: The equation to be solved is

p V d n p = - ^ = 2.44
J il
From Table V, p. 32, of Jahnke and Emde, (3 = 1.135, 3 .7 2 2 ,....

rp~ I 490
P=colJ^ = 5000wW ------------ 7-------- ------------ = 0.470 w

V G V 12 X 10^ X 12' X 32.2
By solving for ca, the first two natural frequencies are

a>i = — 2.41 ra d /s = 0.384 cps
3.722
= 7.93 ra d /s = 1.26 cps
0.470

9.4 VIBRATION OF SUSPENSION BRIDGES

Figure 9.4-1 shows the violent torsional oscillation of the Tacoma Narrows Bridge
just prior to its collapse on November 7, 1940. The bridge had been plagued by a
number of different modes of vibration under high winds ever since it was opened
on July 1, 1940. During its short life of only four months, its unusual behavior had