# Natural frequencies - theoretical vs COSMOS results

## Main Question or Discussion Point

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 dimention:

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 isnt 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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FredGarvin
What was different from your hand calcs? Could you possibly be off by a factor of $$2\pi$$?

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.

FredGarvin
What's the height of the beam?

height = depth = 30mm

Mech_Engineer
Gold Member
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 [Broken]

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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

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