Calculate beam longitudinal natural vibration frequency for modes 1 to 8.
The longitudinal natural vibration frequency for a beam can be calculated by
`fn = k / (2 L) √(E / ρ) `
where :
fn = natural frequency [Hz]
k = mode factor
L = beam length
E = beam elastic modulus
ρ = beam density
The mode factor k is dependent on the mode number and the beam end type. The longitudinal natural frequency is independent of the cross section profile. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes.
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References :
Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill
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