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MECH 375 MECHANICAL VIBRATIONS FINAL CRASH PART 3- vibration measurement and application.vibration control.vibration under general forcing conditions Concordia University CA$17.64
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MECH 375 MECHANICAL VIBRATIONS FINAL CRASH PART 3- vibration measurement and application.vibration control.vibration under general forcing conditions Concordia University
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MECH 375 MECHANICAL VIBRATIONS FINAL CRASH PART 3- vibration measurement and tion tion under general forcing conditions Concordia University

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  • November 21, 2023
  • 19
  • 2023/2024
  • Exam (elaborations)
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  • mech 375
  • mech 375 mechanical vibrations
  • mech 375 concordia university

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MECH 375: MECHANICAL VIBRATIONS FINAL CRASH PART 3-
vibration measurement and application.vibration
control.vibration under general forcing conditions Concordia
University

,Vibration Measurement and Application
Vibration Pickups
The system’s ODE is:

𝑚𝑥 + 𝑐(𝑥 − 𝑦) + 𝑘(𝑥 − 𝑦) = 0

Note that from relative motion:

𝑥 =𝑦+𝑧

Therefore,

𝑚𝑧 + 𝑐𝑧 + 𝑘𝑧 + 𝑚𝑦 = 0

Note that Z is the measured value in vibration pickups.

By finding the transfer function of the system:

𝜔 2
𝑍 ( )
= 𝜔𝑛
𝑌 2 2 2
√(1 − ( 𝜔) ) + (2Ç 𝜔 )
𝜔𝑛 𝜔𝑛

Accelerometer

From the transfer function above and rearranging:

𝑍𝜔𝑛2 1
2
=
2
𝑌𝜔 √(1 − ( 𝜔 2
𝜔 2

𝜔𝑛) ) + (2Ç 𝜔𝑛)

Recall that the terms Xω2 is a variation of acceleration. Therefore Yω2 is the acceleration of the base and
Zωn2 is the measured acceleration.




2

, Vibration Control
Vibration Absorbers
Notice that for a harmonically excited 1 DOF system vibrating at the natural frequency, the response is
becomes catastrophic and leads towards unwanted failure. To avoid this failure, vibration absorbers are
used. Vibration absorbers are basically a mass-spring system attached to the main vibrating body. A 1
DOF problem becomes a 2 DOF problem. As a result, the natural frequency will shift.

The ratio of the magnitudes of both bodies is:

X1
|𝐷1
2 = 2
|X |𝐷
|

Some design considerations include:

 The amplitude X1 = 0. It is usually undesired that the main body has violent vibrations.
 The frequency of the vibration absorber is designed to have the same frequency as the input
frequency.




3

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