Resonant behaviour of damped beam

AI Thread Summary
The quality factor (Q) of a cantilever beam vibrating in air is determined by the damping factor (ζ), with the relationship Q = 1/(2ζ) for small damping values (ζ ≤ 0.1). To calculate Q, one must first define the loading conditions, including the self-mass of the beam. The equivalent viscous damping is influenced by the surrounding fluid medium, which is crucial for accurate calculations. The expressions for Q are applicable to both micro and nano cantilevers, though specific considerations may be necessary for these smaller scales. Understanding these principles is essential for analyzing the resonant behavior of damped beams.
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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