DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION
(FROM BASE TO MASS)
10
9
8
Z

7
6
X
0.01
0.1
5
0.5
4
3
2
1
0
0
1
2
3
4
r
Relative / base
Absolute / base
Amplification of displacement amplitude (transmissibility
of displacement amplitude)
2
DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION
(FROM BASE TO MASS)
m=100kg
vib iso 01.SLDASM
Absolute / base
k = 3125N/m
k = 10000N/m
k = 18000N/m
DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION
(FROM BASE TO MASS)
Problem 1
Mass
Stiffness
100kg
10N/m
Damping
0%
Base excitation at 120% of resonant frequency
Design linear damper to reduce the amplitude of vibration of mass by 50%
DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION
(FROM BASE TO MASS)
Problem 2
A 20kg lab experiment is to be mounted to a table that is bolted to the floor in a laboratory. Measurements indicate that due to the
operation of a nearby pump that runs at 2000RPM (209.4 rad/s) the table has steady-state displacement 0.25mm. What is the
maximum stiffness of an undamped oscillator, placed between the experiment and the table such that the experiment’s acceleration
amplitude is less that 4m/s^2?
Transmissibility ratio:
Transmissibility ratio of acceleration is the same as
transmissibility ratio of displacement :
FORCE TRANSMISSIBILITY IN BASE EXCITATION
(FROM BASE TO MASS)
kY = F0
FORCE TRANSMISSIBILITY IN FORCE EXCITATION
(FORCE TRANSMITTED FROM MASS TO BASE)
r
Force transmitted to base. Isolation (reduction of force
transmitted to base) occurs only for r > √2
FORCE TRANSMISSIBILITY IN FORCE EXCITATION
(FORCE TRANSMITTED FROM MASS TO BASE)
FT
1
1


F0
1 r2
(1  r 2 ) 2
Problem 3
1
 0.25
2
1 r
1
 0.25
r 2 1
r  2.24
What is the minimum static deflection
of an undamped isolator to provide at
least 75% isolation to a pump that
operates at speed between 1500 and
2000RPM (157-209.4 rad/s).
No solution
Isolation is better for higher speeds,
therefore if we ensure 75% isolation at
n 
1500RPM it will be only better at

r
 70
2000RPM
Relation between natural frequency
and operating frequency ω = 157rad/s
(1500RPM). This is the maximum
natural frequency if we want 75%
isolation.
k  n m
2
d static 
8
mg
g
9.81


 0.002
2
2
4900
n m n
FORCE TRANSMISSIBILITY IN FORCE EXCITATION
Problem 4
(FORCE TRANSMITTED FROM MASS TO BASE)
A 150kg machine operates at 1200RPM. It has rotating unbalance 0.45kgm. What is the maximum stiffness of an undamped
isolator such that the force transmitted to the machine’s foundation is less than 2000N
FORCE TRANSMISSIBILITY IN FORCE EXCITATION
(FORCE TRANSMITTED FROM MASS TO BASE)
Problem 5