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eng.beam-natural-frequency-Euler Calculator
Calculates the natural frequency of a simply supported, cantilever, or fixed-fixed beam from section properties and mass per unit length using the Euler-Bernoulli beam equation. The fundamental mode frequency of a simply supported beam is π²/L² × √(EI/m) — stiffening the beam or reducing mass increases natural frequency.
Inputs
E Gpa
Reference formula or conversion factor shown for context.
I Cm4
Two-dimensional surface extent (m²). For complex shapes, break into simpler sub-shapes and sum.
Rho Kg M3
Mass per unit volume (kg/m³). Water: 1,000. Air: 1.225. Steel: 7,850. Affects buoyancy, flow, and structural loads.
A Cm2
Two-dimensional surface extent (m²). For complex shapes, break into simpler sub-shapes and sum.
L M
Distance between supports (m). Longer spans experience larger bending moments — structural adequacy must be rechecked.
Bc
Reference formula or conversion factor shown for context.
Results
1st natural frequency f₁ (Hz)
Frequency at which the structure resonates freely (Hz). If machinery operates near this, resonance can amplify vibrations dangerously. Engineers detune structures to avoid it.
2nd natural frequency f₂ (Hz)
Frequency at which the structure resonates freely (Hz). If machinery operates near this, resonance can amplify vibrations dangerously. Engineers detune structures to avoid it.