natural frequency for cantilever beam mounted on a vibration isolation pad

[Cheetos]

The problem I have is finding the natural frequency for a cantilever beam mounted on a vibration isolation pad. I first modeled a cantilever beam fixed at one end and found the natural frequency using the standard formula Link Based on the frequency, I simplified the system into a mass spring system, by back calculating a stiffness value k1 using f = sqrt(k1/m). Now, assuming my vibration isolation pad has a stiffness value of k2. I add a spring with spring constant k2 in between the cantilever beam and the ground. I thought I can get a keq (k1*k2/(k1+k2)) and then find the new natural frequency or the system. But when I check it using ANSYS WB, I didn't get anything close to it.

 

[boyze]

total beam mass isn't modal mass in this case which appears to be what you have assumed

Have Fun!

James A. Pike

http://www.xl4sim.com

http://www.erieztechnologies.com

 

[Cheetos]

Hmmm.. one question i do have is the deflection and stiffness direction. for a regular mass and spring system, the spring stiffness and deflection are in the same direction as the mass's motion. for the cantilever beam, i know the end of the beam will swing back and forth in the direction perpendicular to the axis of the beam. maybe i can't just simplify the system down to sqrt(k1/m) because the motion is not the same?

 

[boyze]

If you web search on "modal mass of a cantilever beam" and you should find a solution to the "modal" mass. You can then use k/m to find the modal k from fn. However, when you add another stiffness to the system the modal parameters will change. I.e., the mass at the fixed end contributes very little to the mode. Whereas the mass at the free end contributes the most. When you add flexibility at the fixed end then that mass will contribute more.

What is your goal? Check the FE model?

Have Fun!

James A. Pike

http://www.xl4sim.com

http://www.erieztechnologies.com

 

[Cheetos]

thanks james for the tip. i didn't think about that. my actual problem is a vertical motor with a vibration problem. i would like to install vibration isolators underneath the motor to shift or damp out the response. vertical motor acts like a cantilever beam, so the first mode tends to rock back and forth. i got the first mode from the bump test. instead of modeling the entire machine in ANSYS, i thought i could use the equivalent spring method to predict the frequency shift after installing the isolators. before i do that, i wanted to check my assumption, so i used a simple cantilever beam example and checked it against ANSYS. obviously, it showed that i was wrong in my assumption. i decided to work on this cantilever problem until i fully understand what's going on.

in ANSYS WB, i just put a longitudinal spring at one end of the cantilever beam and the frequency changed significantly. when the beam was fixed on one end, the frequency was ~10Hz. with the spring, the frequency changed to 65Hz even though i varied the stiffness between 1e-11 lbf/in to 1e20 lbf/in. i was surprised that a spring can change the frequency that much and also even thought i varied the stiffness, it didn't have much effect. that's why i start to suspect that i probably didn't model the system correctly. don't know if you have any suggestions.

 

[boyze]

Is the mode being excited by the motor 1P speed? Is the motor driving a pump or other device and if so how is the pump or other device attached to the motor? How is the system grounded? We have done many motor pump frequency surveys and have found that it's preferable to build a 3D model of the system including all the relevant structure and masses. Usually the motor can be treated as a rigid mass tuned to it's reed frequency if that is known. Many times the other structure is more complicated. Also, the attachment is many times important and is usually softer than expected. You then need to find a way to move the fn(s) away from the operating range. Soften (reduce fn) is one way. Another is to stiffen (increase fn). Be careful that a higher mode isn't moved into the operating speed range. As you are trying this is where the model becomes very valuable for analytically testing options.

Have Fun!

James A. Pike

http://www.xl4sim.com

http://www.erieztechnologies.com