3.6 Vibration Isolation and Transmissibility
77
Transmissibility is given by Eq. (3.33) as
T R =
1 + ( 2η ζ ) 2
( 1 − η 2 ) 2 + ( 2η ζ ) 2
=
1 + ( 2 × 0.2 × 1.047 ) 2
( 1 − 1.047 2 ) 2 + ( 2 × 0.2 × 1.047) 2
The force transmitted to the foundation is
F T = 2.523
438.65
= 1106.71 N
3.7 Energy Dissipation by Damping
We have seen in the earlier section that the amplitude of motion goes on reducing
with each successive cycle in damped free vibration. This suggests the occurrence
of a loss of energy.
For viscous damping, the damping force is
F 0 = c ˙
x
(3.38)
Let us assume the displacement of the spring–mass system as
x = A sin ( pt− ∈)
(3.39)
and the velocity is
˙
x = Ap cos ( pt− ∈)
(3.40)
Further,
dx = ˙
x dt
(3.41)
The energy dissipated by viscous damping in one such cycle is given by
E d =
F D dx =
2 π
p
0
(cx) dx =
2 π
p
0
(c ˙
x) ˙
x dt