Related Resources: vibration

Beam Spring Fixed and Free End Angular Natural Frequency Equations and Calculator

Machine Design and Engineering

Beam Spring Fixed and Free End with Concentrated Mass Loads Angular Natural Frequency Equations and Calculator

ω_n = [ ( 3 E I ) / ( l³ ( m + 0.23 m_b ) ] ^(1/2)

Where:

m = Mass of Load ( lb-sec² / in ),
m_b = Mass of Beam Spring ( lb-sec² / in ),
l = Length of Beam Spring (in),
I = Area Moment of Inertia of Beam Cross Section (in⁴)
E = Young's Modulus ( lb / in² ),
ω_n = Angular Natural Frequency ( rad / sec )

Related and Useful Links:

• AISC Steel Construction Shapes Properties Viewer
• Young's Modulus on Common Engineering Materials

Reference Harris, Shock and Vibration Handbook