Page 105 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

102 Chapter 1 Fundamentals oF Vibration
Fourier series expansion
example 1.19
Determine the Fourier series expansion of the motion of the valve in the cam-follower system shown
in Fig. 1.61.

Solution: If y(t) denotes the vertical motion of the pushrod, the motion of the valve, x(t), can be
determined from the relation:
y1t2 x1t2
tan u = =
l 1 l 2
or
l 2
x1t2 = y1t2 (E.1)
l 1
where
t
y1t2 = Y ; 0 … t … t (E.2)
t
2p
and the period is given by t = . By defining
v
Yl 2
A =
l 1
y(t)
Rocker arm
u
O
l 1 l 2
Pushrod x(t)
Valve
spring
Valve

y(t)
Roller
follower
Y

0 t
v t 2t 3t

FiGure 1.61 Cam-follower system.