Resonant behaviour of damped beam

[laxman.kosuru]

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

 

[AlephZero]

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.