Natural frequencies - theoretical vs COSMOS results

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Discussion Overview

The discussion revolves around the discrepancies between natural frequency values obtained from COSMOSWorks and those calculated by hand for a cantilever beam. Participants explore the theoretical underpinnings of vibrational modes and seek to understand the differences in results.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The original poster (OP) reports natural frequencies from COSMOSWorks and notes significant differences from hand calculations.
  • Some participants suggest that the discrepancy might be due to a factor of 2π, which converts rad/s to Hz.
  • The OP indicates that their hand calculations yield a first frequency of 5Hz compared to COSMOS's 15Hz, highlighting a substantial difference.
  • Another participant mentions modeling the beam in ANSYS and obtaining results consistent with COSMOS, suggesting the validity of the software's output.
  • A participant shares a resource that provides analytical derivations for vibrational modes of cantilever beams, potentially aiding in understanding the calculations.
  • The OP later acknowledges that the issue was resolved by considering the mode constant, referencing suggestions from both a paper and a book that provided different mode values.

Areas of Agreement / Disagreement

Participants express differing views on the reasons for the discrepancies in frequency values. While some propose potential factors affecting the calculations, the discussion remains unresolved regarding the exact cause of the differences.

Contextual Notes

The discussion highlights the importance of understanding mode constants and their impact on frequency calculations, as well as the potential for software discrepancies in modeling vibrational modes.

WillySaw
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Hi all,

I am new to the forum and am despreate for the solution for my current task. I am given a canteliver beam with the dimension:

L =1250mm
W= 75mm
D= 30mm
E=200 Gpa
density = 7800kg/m^3
poison ratio=0.3

and I optained the first five natural frequencies from COSMOSWorks 2007, which are 15.7483, 39.2254, 98.4208, 241.795 and 274.422Hz respectively. Looks logical isn't it? However, these values are different from the hand calculated values and I really need to find out why.

The formula I used for hand calculation:

W^2=(1.875^4)(EI/density*area*length^4)
where I = (1/12)(bt^3)

Help needed, urgent! Many thanks in advance
 
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What was different from your hand calcs? Could you possibly be off by a factor of [tex]2\pi[/tex]?
 
1st frequency for example, hand calculations give 5Hz while generated value shows 15Hz. This is a huge difference, and I need to know why if it is supposed to be different.

2 pie converts rad/s to Hz, not a crucial point in this case.
 
What's the height of the beam?
 
height = depth = 30mm
 
I modeled up the beam in ANSYS and got the same results for the vibrational modes that you got in COSMOS.

Perhaps this paper can help, it goes through the analytical derivation of vibrational modes for a cantilever beam.

http://em-ntserver.unl.edu/Mechanics-Pages/Scott-Whitney/325hweb/Beams.htm
 
Last edited by a moderator:
Many thanks bro, problem solved! It was due to the mode constant

Scott Whitney's suggestion
Total motion: 325Htot.scm
1st mode: 325h1st.scm
2nd mode: 325h2nd.scm
3rd mode: 325h3rd.scm
4th mode: 325h4th.scm

Book's suggestion (I tried with this and got it)
1st mode: 3.52
2nd mode: 22
3rd mode: 61.7
 
Last edited:

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