Natural Frequency of Each Cable Calculator

Natural Frequency Formula:

\[ \omega_n = \frac{n}{\pi \cdot L_{span}} \cdot \sqrt{\frac{T \cdot g}{q}} \]

Fundamental Vibration Mode (n):

Cable Span (L_span):

Cable Tension (T):

Uniformly Distributed Load (q):

N/m

Natural Frequency (ω_n):

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1. What is Natural Frequency of Cable?

Natural frequency is the frequency at which a cable tends to oscillate when disturbed from its equilibrium position. It is a fundamental property that depends on the cable's physical characteristics and tension.

2. How Does the Calculator Work?

The calculator uses the natural frequency formula:

\[ \omega_n = \frac{n}{\pi \cdot L_{span}} \cdot \sqrt{\frac{T \cdot g}{q}} \]

Where:

\( \omega_n \) — Natural frequency (Hz)
\( n \) — Fundamental vibration mode
\( L_{span} \) — Cable span (m)
\( T \) — Cable tension (N)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( q \) — Uniformly distributed load (N/m)

Explanation: The formula calculates the natural frequency based on cable properties and vibration mode, considering the balance between tension and distributed load.

3. Importance of Natural Frequency Calculation

Details: Calculating natural frequency is crucial for cable structure design, vibration analysis, and preventing resonance effects that could lead to structural failure.

4. Using the Calculator

Tips: Enter fundamental vibration mode, cable span in meters, cable tension in Newtons, and uniformly distributed load in N/m. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is fundamental vibration mode?
A: Fundamental vibration mode (n) is an integer value representing the mode of vibration, typically starting from 1 for the fundamental mode.

Q2: Why is natural frequency important in cable design?
A: It helps engineers avoid resonance conditions where external forces match the cable's natural frequency, which could cause excessive vibrations and structural damage.

Q3: How does cable tension affect natural frequency?
A: Higher tension increases natural frequency, while lower tension decreases it. Tension is a key factor in controlling vibration characteristics.

Q4: What is uniformly distributed load?
A: UDL is a load that is evenly distributed along the entire length of the cable, typically representing the cable's self-weight or additional distributed loads.

Q5: Can this calculator be used for different vibration modes?
A: Yes, by changing the fundamental vibration mode value, you can calculate natural frequencies for different modes of vibration.