Resonant behaviour of damped beam

In summary, the quality factor Q is a measure of the sharpness of a peak of resonance and also the damping, with a value of 1/(2*zeta) for small damping factors. For mechanical systems, it is important to consider the equivalent viscous damping, which may be related to the surrounding fluid in this case. A helpful resource for further understanding is "Mechanical Vibrations - Theory and Applications" by F. S. Tse, I. E. Morse, and R. T. Hinkle.
  • #1
laxman.kosuru
3
0
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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  • #2
Your first step is to define the loading, including self mass.
 
  • #3
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 [tex]Q[/tex] is a measure of the sharpness of a peak of resonance and also the damping.

For small values of the damping factor [tex]\zeta[/tex], that is, [tex]\zeta \leq 0.1 [/tex],

[tex]
Q = \frac{1}{2 \zeta}
[/tex]

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.
 
  • #4
JolileChat said:
The quality factor [tex]Q[/tex] is a measure of the sharpness of a peak of resonance and also the damping.

For small values of the damping factor [tex]\zeta[/tex], that is, [tex]\zeta \leq 0.1 [/tex],

[tex]
Q = \frac{1}{2 \zeta}
[/tex]

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
 

Related to Resonant behaviour of damped beam

1. What is resonant behavior of a damped beam?

The resonant behavior of a damped beam refers to the phenomenon in which the beam oscillates at a specific frequency due to an external force. This frequency is known as the resonance frequency and is determined by the properties of the beam and the damping force acting on it.

2. How does damping affect the resonant behavior of a beam?

Damping is a force that dissipates the energy of a vibrating system, such as a beam. It reduces the amplitude of the beam's oscillations and shifts the resonance frequency to a lower value. Therefore, damping affects the resonant behavior of a beam by decreasing the amplitude and changing the frequency at which it resonates.

3. What factors influence the resonant behavior of a damped beam?

The resonant behavior of a damped beam is influenced by several factors, including the material properties of the beam (such as stiffness and density), the damping force (such as friction or air resistance), and the external force applied to the beam. The length and geometry of the beam also play a role in determining its resonance frequency.

4. How can the resonant behavior of a damped beam be controlled?

The resonant behavior of a damped beam can be controlled by adjusting the properties of the beam, such as its stiffness and damping force. For example, increasing the stiffness of the beam or adding more damping can shift the resonance frequency to a desired value. Additionally, external devices such as tuned mass dampers can be used to control the resonant behavior of a beam in real-time.

5. Why is understanding the resonant behavior of a damped beam important?

Understanding the resonant behavior of a damped beam is important for several reasons. It helps in the design and construction of structures such as buildings and bridges, as resonance can lead to excessive vibrations that can cause structural failure. Additionally, resonant behavior is also important in fields such as acoustics, where it is utilized in the design of musical instruments and soundproofing materials.

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