Free Engineering Tool

Turbine Blade Natural Frequency & Campbell Check

Calculate the first-mode natural frequency of a turbine blade (cantilever beam model) and check for harmonic crossings within the operating speed range using a simplified Campbell diagram.

Cantilever Beam Model Campbell Diagram Harmonics 1×–12×

Blade Length (mm)

Blade Thickness (mm, in bending direction)

Blade Width (mm, chord)

Material

Number of Blades

Min Speed (RPM)

Max Speed (RPM)

Quick presets

Results

First Mode Natural Frequency (f₁)

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Second Mode (f₂ ≈ 6.27 × f₁)

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Third Mode (f₃ ≈ 17.55 × f₁)

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Harmonic Crossings in Speed Range

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Blade Passing Frequency (at max RPM)

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Cantilever Beam Natural Frequency

A turbine blade can be modeled as a cantilever beam fixed at the root. The natural frequencies are:

λ_n — eigenvalue: λ₁ = 1.8751, λ₂ = 4.6941, λ₃ = 7.8548
E — Young’s modulus (Pa)
I — second moment of area (m⁴) = b·h³/12 for rectangular cross-section
ρ — material density (kg/m³)
A — cross-sectional area (m²) = b·h
L — blade length (m)

Campbell Diagram

The Campbell diagram plots blade natural frequency (horizontal lines) against engine order excitation lines (diagonal lines: f = n × RPM/60). Intersections within the operating speed range indicate potential resonance.

A minimum 10% separation margin between natural frequencies and excitation frequencies at operating speed is generally required.

Mode Shape Ratios

Mode	λ_n	f_n / f₁ ratio	Character
1st	1.8751	1.000	First bending
2nd	4.6941	6.267	Second bending
3rd	7.8548	17.55	Third bending

Example — Steam Turbine LP Blade

Given: L = 500 mm, thickness h = 12 mm, width b = 80 mm, Steel (E = 200 GPa, ρ = 7850 kg/m³)

I = 80 × 12³ / 12 = 11,520 mm⁴ = 1.152 × 10⁻⁸ m⁴

A = 80 × 12 = 960 mm² = 9.6 × 10⁻⁴ m²

f₁ = (1.8751² / (2π)) × √(200×10⁹ × 1.152×10⁻⁸ / (7850 × 9.6×10⁻⁴ × 0.5⁴))

f₁ ≈ 44.8 Hz

⚠️ Note: This is a simplified uniform cantilever beam model. Actual turbine blades have tapered profiles, twist, shrouds, platform effects, centrifugal stiffening, and temperature-dependent material properties that significantly affect natural frequencies. Use FEA for detailed design.

Turbine Blade Natural Frequency & Campbell Diagram Calculator

Published by Nikolai Shelkovenko on February 15, 2026 March 5, 2026

Results

Cantilever Beam Natural Frequency

Campbell Diagram

Mode Shape Ratios