Resonant behaviour of damped beam

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Discussion Overview

The discussion centers around the calculation of the quality factor for a cantilever beam that is vibrating in air or other mediums. Participants explore the theoretical aspects of quality factor expressions and their applicability to micro and nano cantilevers, as well as the influence of damping in these systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks guidance on finding the quality factor of a cantilever beam and expresses confusion regarding the relevant literature on beam vibrations.
  • Another participant suggests that the first step involves defining the loading conditions, including the self mass of the beam.
  • A participant provides a formula for the quality factor Q, stating that for small damping factors (\zeta ≤ 0.1), Q can be calculated as Q = 1/(2ζ).
  • It is mentioned that the equivalent viscous damping may be related to the fluid surrounding the beam.
  • There is a request for the specific expression of the quality factor for a cantilever beam in air medium.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specific expression for the quality factor in air medium, and multiple viewpoints regarding the calculation and factors influencing the quality factor remain present.

Contextual Notes

There are limitations regarding the assumptions made about damping and the definitions of the quality factor, which may vary based on the specific conditions of the cantilever beam and the medium in which it vibrates.

Who May Find This Useful

This discussion may be of interest to students and researchers working on mechanical vibrations, particularly those focusing on cantilever beams and their behavior in various mediums.

laxman.kosuru
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hi all
i have a problem in finding the quality factor of cantilever beam (one end is fixed and other end is free ) vibrating in air /other medium? how the qualtiy factor expression for beam is calculated? whether all these expressions applicable to micro and nano cantilevers.
please explain me.
i am new to this area. i read books on vibrations of beam. i didnt get anything
please mention steps for finding quality factor of cantilever beam in air medium(damped system)
Thanks
 
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Your first step is to define the loading, including self mass.
 
laxman.kosuru said:
hi all
i have a problem in finding the quality factor of cantilever beam (one end is fixed and other end is free ) vibrating in air /other medium? how the qualtiy factor expression for beam is calculated? whether all these expressions applicable to micro and nano cantilevers.
please explain me.
i am new to this area. i read books on vibrations of beam. i didnt get anything
please mention steps for finding quality factor of cantilever beam in air medium(damped system)
Thanks

The quality factor Q is a measure of the sharpness of a peak of resonance and also the damping.

For small values of the damping factor \zeta, that is, \zeta \leq 0.1,

<br /> Q = \frac{1}{2 \zeta}<br />

For mechanical systems, it is useful to get a measure of the equivalent viscous damping. In your case, it might be related to the fluid around the beam.

A good reference is:
F. S. Tse, I. E. Morse and R. T. Hinkle. Mechanical Vibrations - Theory and Applications.
 
JolileChat said:
The quality factor Q is a measure of the sharpness of a peak of resonance and also the damping.

For small values of the damping factor \zeta, that is, \zeta \leq 0.1,

<br /> Q = \frac{1}{2 \zeta}<br />

For mechanical systems, it is useful to get a measure of the equivalent viscous damping. In your case, it might be related to the fluid around the beam.

A good reference is:
F. S. Tse, I. E. Morse and R. T. Hinkle. Mechanical Vibrations - Theory and Applications.

Thanks jolile
could you please give me the expression for cantilever q factor in air medium
 

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