Resonant behaviour of damped beam

In summary, calculating the quality factor for a cantilever beam vibrating in air or other medium is a complex process that involves measuring the Q factor and using design values. The Q factor can be affected by various physical mechanisms such as material properties and friction, and can vary greatly even with small changes. Mathematical models can be used to approximate the damping, but ultimately it is best to refer to similar research and experiments in order to accurately determine the Q factor for a specific cantilever beam.
  • #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
 
Physics news on Phys.org
  • #2
Some structures (for example shock absorbers) are intended to have a low Q factor and this can usually be calculated from the design. However there is no simple way to calculate the Q factor for lightly damped structures. In practice, you measure the Q factors and use design values based on that.

There are several different physical mechanisms that dissipate the energy when a structure vibrates. Three important ones are

1. The material is not perfectly elastic. Some of the strain energy in each vibration cycle is converted to heat. This is called "hysteretic damping".
2. If a structure is made from several parts connected together, energy can be lost by friction at the joints, etc.
3. The motion of the surface of the structure radiates energy into the air as sound (possibly infrasound and ultrasound as well as audible frequencies).

For lightly damped structures, the Q values can be very sensitive to small changes. For example, a simple steel cantilever beam (say 100mm x 10mm x 1mm) clamped at one end and vibrating in air may have a Q of 100 or more. But if there is some oil or grease on the surface that is clamped, the Q may fall from 100 to 10.

Mathematical models like "modal damping" or "Rayleigh damping" are not based on the physics of what causes the damping. They are just conveniient ways to create a mathematical model fitted to experimental measurements

Look for papers on structures with similar types of micro or nano cantilevers to yours, and see how they model the damping.
 

Related to Resonant behaviour of damped beam

What is resonant behaviour of damped beam?

Resonant behaviour of damped beam refers to the phenomenon where a beam, when subjected to a periodic force, vibrates with a large amplitude at a specific frequency, known as the resonant frequency.

What factors affect the resonant behaviour of damped beam?

The resonant behaviour of damped beam is affected by various factors including the material properties of the beam, its geometry, damping coefficient, and the applied force. These factors determine the natural frequency of the beam and its response to external forces.

How is the resonant frequency of a damped beam calculated?

The resonant frequency of a damped beam can be calculated using the formula: f = (1/2π) x √(k/m), where f is the resonant frequency, k is the stiffness of the beam, and m is the mass of the beam.

What is the significance of understanding resonant behaviour of damped beam?

Understanding the resonant behaviour of damped beam is crucial in designing structures that can withstand external forces without experiencing excessive vibrations or damage. It also helps in predicting the natural frequency of a structure and avoiding resonance, which can lead to catastrophic failure.

How can the resonant behaviour of damped beam be controlled?

The resonant behaviour of damped beam can be controlled by adjusting the material properties, geometry, and damping coefficient of the beam. Adding additional supports or altering the external force can also help in controlling the resonant behaviour of a damped beam.

Similar threads

Elasticity of a Tubular Cantilever Beam
    • General Engineering
Replies
8
Views
1K
Critically damped cantilever beam
    • Mechanical Engineering
Replies
2
Views
1K
Resonant behaviour of damped beam
    • Mechanical Engineering
Replies
3
Views
3K
Closed form solution for second order beam deflection?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Inclined Beam w/ UDL Homework Statement
    • Engineering and Comp Sci Homework Help
Replies
4
Views
8K
Engineering Struggling with a Structural Analysis Problem?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
897
How to find cross sectional dimension of beam
    • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
Vibration of a cantilever beam problem
    • Introductory Physics Homework Help
Replies
2
Views
1K
Vibrations in cantilever beams
    • Mechanical Engineering
Replies
2
Views
2K
Mechanical-Structural Engineering: Forces/Moments on Complex Beam
    • Engineering and Comp Sci Homework Help
Replies
23
Views
4K

Hot Threads

Recent Insights

Back
Top