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Finding the natural frequency of a steel beam

  • Thread starter hks118
  • Start date
  • #1
19
0

Homework Statement


I am trying to calculate the natural frequency of a steel beam.


Homework Equations


I=1/12*W*T^3
Volume= T*W*L
M0=V*ρ
K=(3EI/L^3)
Meff=(33/140)*M0+Mend
ωn=√(k/Meff)

The Attempt at a Solution


This should be a simple plug and chug problem but I can't see what I'm doing wrong.

L=0.4572m
W=0.026035m
T=0.006223m
E= 3*10^6
ρ=7850kg/m^3

Mend=.025kg


I=5.22848E-10

V=7.41E-05 m^3

M0=5.81E-01

K=0.049237907

Meff=2.43E-01

ωn=0.450088787 Hz

But this is way off from my experimental value of around 20Hz. Everything is in kg and m.
 

Answers and Replies

  • #2
322
0


Sorry to ask this , what is K and what is E? and their units
 
  • #3
121
0


Your modulus of elasticity appears to have units of psi. Change it to N/m^2 & you'll fix your problem.
 
  • #4
1
0


natural frequency = (square root)k/m
 
  • #5
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,666


E for steel is 3*10^7 psi (30,000,000 psi) not 3,000,000 psi
 

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