Page 132 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

problems 129
1.38* Design a steel helical compression spring to satisfy the following requirements:
Spring stiffness 1k2 Ú 8000 N>mm
Fundamental natural frequency of vibration 1f 1 2 Ú 0.4 Hz
Spring index 1D>d2 Ú 6
Number of active turns 1N2 Ú 10.
The stiffness and fundamental natural frequency of the spring are given by [1.43]:

Gd 4 1 kg
k = and f 1 =
3
8D N 2A W
where G = shear modulus, d = wire diameter, D = coil diameter, W = weight of the
spring, and g = acceleration due to gravity.

1.39 Find the spring constant of the bimetallic bar shown in Fig. 1.89 in axial motion.

2 cm Steel,
9
E 207 10 Pa
0.5 cm
Aluminum,
9
0.5 m E 83 10 Pa
x

y

FiGure 1.89 A bimetallic bar in axial motion.

1.40 Consider a spring of stiffness k stretched by a distance x 0 from its free length. One end of the
spring is fixed at point O and the other end is connected to a roller as shown in Fig. 1.90. The

O

k

A B
x

FiGure 1.90 One end of
spring with lateral movement.