100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
MECH 375 MECHANICAL VIBRATIONS FINAL CRASH PART 3- vibration measurement and application.vibration control.vibration under general forcing conditions Concordia University CA$16.59   Add to cart
Quickly navigate to
Preview
  2.  
  3. Concordia University ( )

Exam (elaborations)

MECH 375 MECHANICAL VIBRATIONS FINAL CRASH PART 3- vibration measurement and application.vibration control.vibration under general forcing conditions Concordia University
 4 views  0 purchase
  • Course

MECH 375 MECHANICAL VIBRATIONS FINAL CRASH PART 3- vibration measurement and tion tion under general forcing conditions Concordia University

Preview 3 out of 19  pages

Document information

  • November 21, 2023
  • 19
  • 2023/2024
  • Exam (elaborations)
  • Unknown

Subjects

  • mech 375
  • mech 375 mechanical vibrations
  • mech 375 concordia university

Written for

Seller

avatar-seller
smartzone

Reviews received

Content preview

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

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller smartzone. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for CA$16.59. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

76658 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
CA$16.59
  • (0)
  Add to cart