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DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION (FROM BASE TO MASS). Z. X. r. Relative / base. Absolute / base. Amplification of displacement amplitude (transmissibility of displacement amplitude). DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION (FROM BASE TO MASS). m=100kg.

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slide2

DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION

(FROM BASE TO MASS)

Z

X

r

Relative / base

Absolute / base

Amplification of displacement amplitude (transmissibility of displacement amplitude)

slide3

DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION

(FROM BASE TO MASS)

m=100kg

vibiso 01.SLDASM

Absolute / base

k = 3125N/m

k = 10000N/m

k = 18000N/m

slide4

DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION

(FROM BASE TO MASS)

Problem 1

Mass 100kg

Stiffness 10N/m

Damping 0%

Base excitation at 120% of resonant frequency

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

slide5

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 :

slide7

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

slide8

FORCE TRANSMISSIBILITY IN FORCE EXCITATION

(FORCE TRANSMITTED FROM MASS TO BASE)

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

No solution

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

slide9

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

slide10

FORCE TRANSMISSIBILITY IN FORCE EXCITATION

(FORCE TRANSMITTED FROM MASS TO BASE)

Problem 5