Natural Frequency Calculator Beam

Beam Natural Frequency Equation:

\[ f = \frac{\beta^2}{2\pi} \sqrt{\frac{EI}{\mu L^4}} \]

Mode Factor (β):

dimensionless

Young's Modulus (E):

Moment of Inertia (I):

m⁴

Mass per Unit Length (μ):

kg/m

Beam Length (L):

Natural Frequency (f):

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1. What is Beam Natural Frequency?

The natural frequency of a beam is the frequency at which it tends to vibrate when disturbed. It's a fundamental property of the beam's structure that depends on its material properties, geometry, and boundary conditions.

2. How Does the Calculator Work?

The calculator uses the beam natural frequency equation:

\[ f = \frac{\beta^2}{2\pi} \sqrt{\frac{EI}{\mu L^4}} \]

Where:

\( f \) — Natural frequency (Hz)
\( \beta \) — Mode factor (dimensionless, depends on boundary conditions)
\( E \) — Young's modulus (Pa)
\( I \) — Area moment of inertia (m⁴)
\( \mu \) — Mass per unit length (kg/m)
\( L \) — Length of the beam (m)

Explanation: The equation relates the beam's stiffness (EI) to its mass distribution (μ) and length, with the mode factor accounting for vibration mode and boundary conditions.

3. Importance of Natural Frequency Calculation

Details: Calculating natural frequency is crucial for avoiding resonance in structures, designing vibration-resistant systems, and analyzing dynamic behavior in mechanical and civil engineering applications.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Typical β values: 1.875 (first mode, cantilever), 3.142 (first mode, simply supported), 4.730 (first mode, fixed-fixed).

5. Frequently Asked Questions (FAQ)

Q1: What are typical mode factor (β) values?
A: For fundamental frequency: 1.875 (cantilever), 3.142 (simply supported), 4.730 (fixed-fixed), π (free-free).

Q2: How does beam length affect frequency?
A: Frequency is inversely proportional to L² - doubling length reduces frequency by factor of 4.

Q3: What if my beam has variable cross-section?
A: This equation is for uniform beams. For variable sections, use numerical methods like FEM.

Q4: Does this account for damping?
A: No, this calculates undamped natural frequency. Damping slightly reduces actual vibration frequency.

Q5: How accurate is this for real-world beams?
A: It's accurate for ideal, slender beams. Real-world factors like joints, imperfections, and non-uniformities may affect results.