Finding the natural frequency of a steel beam

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SUMMARY

The discussion focuses on calculating the natural frequency of a steel beam using specific formulas and parameters. The user provided dimensions and material properties, including length (L = 0.4572 m), width (W = 0.026035 m), thickness (T = 0.006223 m), Young's modulus (E = 3 x 10^6 psi), and density (ρ = 7850 kg/m³). The calculated natural frequency (ωn) was found to be approximately 0.45 Hz, which significantly deviates from the expected experimental value of around 20 Hz. The key issue identified was the incorrect unit conversion for Young's modulus, which should be 3 x 10^7 psi (30,000,000 psi) instead of 3 x 10^6 psi.

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  • Understanding of beam mechanics and natural frequency calculations
  • Familiarity with material properties, specifically Young's modulus and density
  • Knowledge of basic physics equations related to oscillation and stiffness
  • Proficiency in unit conversions, particularly between psi and N/m²
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  • Research the calculation of natural frequencies for different beam configurations
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Mechanical engineers, structural analysts, students studying dynamics, and anyone involved in the design and analysis of beam structures will benefit from this discussion.

hks118
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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.
 
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Sorry to ask this , what is K and what is E? and their units
 


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


natural frequency = (square root)k/m
 


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

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