Amplification of displacement amplitude (transmissibility of displacement amplitude)

2Amplification of displacement amplitude (transmissibility of displacement amplitude)

DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION

(FROM BASE TO MASS)

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4

0.010.10.5

Relative / base

Absolute / base

XZ

r

k = 3125N/m k = 10000N/m k = 18000N/m

m=100kg

vib iso 01.SLDASM

DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION

(FROM BASE TO MASS)

Absolute / base

DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION

(FROM BASE TO MASS)

Problem 1

Mass 100kgStiffness 10N/m

Damping 0%Base excitation at 120% of resonant frequency

Design linear damper to reduce the amplitude of vibration of mass by 50%

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 of acceleration is the same as transmissibility ratio of displacement :

Transmissibility ratio:

DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION

(FROM BASE TO MASS)

FORCE TRANSMISSIBILITY IN BASE EXCITATION

(FROM BASE TO MASS)

kY = F0

FORCE TRANSMISSIBILITY IN FORCE EXCITATION

(FORCE TRANSMITTED FROM MASS TO BASE)

Force transmitted to base. Isolation (reduction of force transmitted to base) occurs only for r > √2

r

8

Problem 3

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).

Isolation is better for higher speeds,

therefore if we ensure 75% isolation at

1500RPM it will be only better at

2000RPM

22 20

2

2

2

2 2

1 11(1 )

1 0.2511 0.2512.24

70

9.81 0.0024900

T

n

n

staticn n

FF rr

r

rr

r

k mmg gdm

No solution

Relation between natural frequency and operating frequency ω = 157rad/s (1500RPM). This is the maximum natural frequency if we want 75% isolation.

FORCE TRANSMISSIBILITY IN FORCE EXCITATION

(FORCE TRANSMITTED FROM MASS TO BASE)

Problem 4

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

FORCE TRANSMISSIBILITY IN FORCE EXCITATION

(FORCE TRANSMITTED FROM MASS TO BASE)