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eng.beam-natural-frequency Calculator
Calculates beam natural frequency and mode shapes from boundary conditions, span, and cross-section using exact solutions. Natural frequency of the first bending mode is the critical frequency for avoiding resonance with machine vibration or footfall loading.
Inputs
L M
Distance between supports (m). Longer spans experience larger bending moments — structural adequacy must be rechecked.
Ei Nm2
Reference formula or conversion factor shown for context.
M Kg Per M
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
Results
first natural frequency ω₁ (rad/s)
Frequency at which the structure resonates freely (Hz). If machinery operates near this, resonance can amplify vibrations dangerously. Engineers detune structures to avoid it.
fundamental frequency f₁ (Hz)
Sample size or count used in the calculation.
period T₁ (s)
Reference formula or conversion factor shown for context.
ω₁ = (π/L)² √(EI/m)
Reference formula or conversion factor shown for context.
2nd mode frequency f₂ (Hz)
The most frequently occurring value.
resonance risk
Overall risk level based on the computed score or classification. Higher risk may call for mitigating actions or additional review.