Cantilever Beam Natural Frequency Calculator

Cantilever Beam Frequency Equation:

\[ f = \frac{1.875^2}{2\pi} \sqrt{\frac{EI}{\mu L^4}} \]

Young's Modulus (E):

Area Moment of Inertia (I):

m⁴

Mass per Unit Length (μ):

kg/m

Beam Length (L):

Natural Frequency (f):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Cantilever Beam Natural Frequency?

The natural frequency of a cantilever beam is the frequency at which the beam will oscillate when disturbed from its equilibrium position. It's a fundamental property that affects the beam's response to dynamic loads and vibrations.

2. How Does the Calculator Work?

The calculator uses the cantilever beam frequency equation:

\[ f = \frac{1.875^2}{2\pi} \sqrt{\frac{EI}{\mu L^4}} \]

Where:

\( f \) — Natural frequency (Hz)
\( E \) — Young's modulus of the material (Pa)
\( I \) — Area moment of inertia of the cross-section (m⁴)
\( \mu \) — Mass per unit length (kg/m)
\( L \) — Length of the beam (m)
1.875 — First mode constant for cantilever beams

Explanation: The equation calculates the fundamental natural frequency of a uniform cantilever beam based on its material properties and geometry.

3. Importance of Natural Frequency Calculation

Details: Knowing the 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 the specified units. Ensure values are positive and physically meaningful. The calculation assumes a uniform, prismatic beam with fixed-free boundary conditions.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of 1.875 in the equation?
A: 1.875 is the first root of the characteristic equation for a cantilever beam's boundary conditions, representing the fundamental vibration mode.

Q2: How does beam length affect natural frequency?
A: Frequency is inversely proportional to the square of the length (f ∝ 1/L²). Doubling the length reduces frequency by a factor of 4.

Q3: What if my beam has a non-uniform cross-section?
A: This calculator is for uniform beams. Non-uniform beams require more complex analysis methods like finite element analysis.

Q4: Does this account for damping?
A: No, this calculates the undamped natural frequency. Damping would slightly reduce the actual oscillation frequency.

Q5: What are typical natural frequency ranges for cantilever beams?
A: It varies widely based on materials and dimensions - from a few Hz for long flexible beams to kHz for short stiff beams.