1. What is Beam Natural Frequency?

The natural frequency of a beam is the frequency at which it tends to oscillate when disturbed from its equilibrium position. This calculator provides the first mode frequency for a simply supported beam.

2. How Does the Calculator Work?

The calculator uses the beam frequency equation:

Where:

• \( f \) — Natural frequency (Hz)
• \( E \) — Young's modulus (Pa)
• \( I \) — Moment of inertia (m⁴)
• \( \mu \) — Mass per unit length (kg/m)
• \( L \) — Beam length (m)
• \( \pi \) — Mathematical constant pi (~3.1416)

Explanation: The equation accounts for the beam's stiffness (EI), mass distribution (μ), and length (L) to determine its fundamental vibration frequency.

3. Importance of Natural Frequency Calculation

Details: Knowing a beam's natural frequency is crucial for avoiding resonance in structural design, which can lead to excessive vibrations and potential failure.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Ensure inputs are positive numbers. The calculation assumes a simply supported beam with uniform cross-section.

5. Frequently Asked Questions (FAQ)

Q1: What boundary conditions does this assume?
A: This calculation is for a simply supported beam. Different boundary conditions (fixed, cantilever) would require different equations.

Q2: Does this include damping effects?
A: No, this is the undamped natural frequency. Damping would slightly reduce the actual vibration frequency.

Q3: What's the range of validity for this equation?
A: It's valid for linear elastic materials and small deflections where the beam theory assumptions hold.

Q4: Can I use this for composite beams?
A: You can use equivalent E and I values for composite beams, but accuracy may vary depending on the material distribution.

Q5: How does this relate to higher vibration modes?
A: Higher modes will have frequencies that are multiples of the fundamental frequency shown here.