Page 549 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

536 Answers to Selected Problems

Kl ^ I FI I El
10-22 k = 5mgl\ = 1.0/2, 1.55W ^ , a;. = 19.02W —^ ,
V ml ^ V ml

0.2875 \
-0.2271/1
0.0375 (
0.0146/)
0.2031 pr
10-27 (b)
192 El
0.0286 pP
16 El

CHAPTER 11

11-3 r ^
' " f i
4|7„/ . 2 x t t
11-8 y(x,i) = .. . sin - ^ ( 1 cos it>2^
ttMcoj '
11-10 Modes absent are 2nd, 5th, 8th, etc.

11-11 r = v/2cos(2n - 1)t7-/6, D„ = (1 —COS iO^t)
cos ( tt/6 ) cos (7t/2 ) ( x//)
AE (v/2)- D,
cos(5 7 r/6 )co s(5 7 r/2 )(jc//) ^
-I ^ u _|_
(577/2)"
1 ri
11-14 r, = jj4>^(.x)dx = 0.784
r, = I j'(f>2(x)dx = 0.434
r, = j j ’<i>^(x)dx = 0.254
^»2(0) ^»p'zCO)

11-19 1 + 1 +
Mo)][i - {o)/o>A
K<p\{0)<p',(Q) Kcp\{0)<p'2Ì0)

- (to/o),)"] —(fti/ftij)"]

, 7T rr TTX
' J = y v2 COS -y -, etc.
‘Pi = 1/2 sir / <PI
One-mode approximation gives
. 2/C /T7\2 El

1 + -----^ T 1 O), = 77'

M(0] \ I I ' MP
One-mmode approximation
11-20 O n e-
>1
(if / Mio] ' I I