Page 67 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

64 Chapter 1 Fundamentals oF Vibration

t

b a
l

d

W W
(a)
W

W
Beam

k b
k eq

Rope k r

W
W

W
(b) (c) (d)

FiGure 1.31 Hoisting drum.

The stiffness of the wire rope subjected to axial loading is
2
AE pd E
k r = = (E.2)
l 4l
Since both the wire rope and the cantilever beam experience the same load W, as shown in Fig. 1.31(b),
they can be modeled as springs in series, as shown in Fig. 1.31(c). The equivalent spring constant k eq
is given by
1 1 1 4b 3 4l
= + = +
2
k eq k b k r Eat 3 pd E
or
3 2
E pat d
k eq = ¢ ≤ (E.3)
2 3
4 pd b + lat 3
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