General Mechanical

General Mechanical

Cantilever beam with heavy mass and spring at the free end

    • Abdulelah
      Subscriber

      Hey, I'm trying to find the frequencies of a cantilever beam with heavy mass and spring attached at the free end as shown in figure.    First, I found the solution without the spring and it was reasonable compared with the analytical solution. However, when I add the spring, the solution doesn't change which mean something is wrong. Anyone have an idea of what might be the problem?    


    • peteroznewman
      Subscriber

      Maybe the spring rate is too insignificant to have an influence on the modal frequency.
      Try increasing the spring rate by 10^6 and see if the modal frequency changes in that case.


      How many modes did you look at?  Make sure to look at a mode that would stretch the spring.

    • Abdulelah
      Subscriber

      Dear Peter, 


      Thanks for your reply. I looked at 13 modes because I'm interested in the first five frequencies and I changed the rate to 4e6 but still nothing happened. Here is a picture of what I did and maybe you can see where my mistake is: 


        


       


      Also, should I choose a material for the spring? cause I simulated with both structural steel and none and got the same result. 

    • peteroznewman
      Subscriber

      Springs don't have materials, just spring rate and damping.


      Please show Mode 1 deformation plot with the spring and with the spring Suppressed.

    • Abdulelah
      Subscriber

      Sorry I couldn't get the plot. Is there a straight forward way to get it?  

    • peteroznewman
      Subscriber

      Insert a Total Deformation plot into the Results.

    • Abdulelah
      Subscriber

      I only found chart but it didn't allow me to assign it to the total deformation 

    • peteroznewman
      Subscriber

      Did you solve the Modal analysis?


      Click on the Solution Folder, do you see the Modal Frequencies in the Tabular Data window?


      Is the first number bigger than zero?


      Right click on that first row and Create Mode Shape Results. Now you have a Total Deformation plot under the Solution folder. Right click on that and Evaluate All Results.


      Take a snapshot of that plot.


       

    • Abdulelah
      Subscriber

      Hopefully this is what you mean


       


      with the spring: 



       


      spring is suppressed: 


    • peteroznewman
      Subscriber

      The spring does make a difference. Look at the two tables side-by-side.


      The spring affects Mode 2 by a lot!


      No Spring on the left.                   Spring on the right.


        

    • Abdulelah
      Subscriber

      you're right the difference in the second mode is big. However, the big difference is happening only in mode 2 as you can see which probably means that I'm doing something wrong. Also, it's far from the analytical solution (which is 207.5hz for mode 2). 


        


      Anyway thanks a lot for your help. I will review everything and will see what happens. 


      Hope you have a good weekend. 

    • Eric_Eric
      Subscriber

      Don't know why you have the same frequency for the first two modes. And it seems the 3rd and 4th frequencies are also the same. It's probably because you are modeling a 3D beam and the first mode is bending mode. For the 3D model, bending modes in y and z-direction should be the same, both of which should be the first mode in theory. That's why you have identical frequencies 14.066 Hz, but they are actually the same modes. Once you add a spring in the y-direction, you change the bending mode in y-direction (2nd mode in your results), but there is no influence on the motion in z-direction (first mode).

    • Abdulelah
      Subscriber
      Yeah I agree with your analysis. The frequencies come in pairs which represent the bending in y and z direction. Since my design is symmetric, the two frequencies should be equal and when I add a spring it would break the symmetry. However, you can see that not all frequencies are in pairs (for example the 5th and the 10th mode) and I think they represent the frequencies of rotation.Note regarding my last post: I think Ansys solution is right and probably the problem is in the equation that I used for my analytical solution. n
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