Page 57 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

54 Chapter 1 Fundamentals oF Vibration

x
O
k 1 k 2
W

c 1 c 2

(a)
Spring force (F)

k (x c )
2
2
k 2
O
Displacement (x)
c 1 c 2

k 1
k (x c )
1
1
(b)
FiGure 1.20 Nonlinear spring force-displacement relation.

F Weightless
rigid bar Spring force (F)
O

c
x F k x k (x c)
2
1
k 1 k 1 F k 1 x
2 2
k 2

x
O
x 0 corresponds to position c Displacement
of force
of the bar with no force
(a) (b)
FiGure 1.21 Nonlinear spring force-displacement relation.