What is damping ratio ζ?

Damping ratio ζ (zeta) is the ratio of actual damping to critical damping. ζ = 0 means undamped, ζ = 1 is critically damped, 0 < ζ < 1 is underdamped (oscillatory). Most mechanical systems have ζ between 0.01 and 0.1.

How does the logarithmic decrement method work?

Measure successive peak amplitudes x₁ and x₂ in free vibration. The log decrement δ = ln(x₁/x₂). For n cycles: δ = (1/n)ln(x₁/xₙ₊₁). Then ζ = δ/√(4π² + δ²) ≈ δ/(2π) for small damping.

How does the half-power bandwidth method work?

From a frequency response function, measure the natural frequency fn and the two frequencies f₁, f₂ where amplitude drops to 1/√2 of peak (−3 dB). Then ζ = (f₂ − f₁)/(2fn) = Δf/(2fn).

Which method is more accurate?

Log decrement is better for lightly damped systems (ζ < 0.1) with clear free vibration decay. Half-power bandwidth works well for forced vibration measurements and moderate damping. For very light damping, averaging over many cycles improves log decrement accuracy.

What is the quality factor Q?

Quality factor Q = 1/(2ζ). A high Q indicates low damping and a sharp resonance peak. Q = 50 means ζ = 0.01. Q is commonly used in acoustics, electronics, and structural dynamics.

Herramienta de ingeniería gratuita #066

Calculadora de relación de amortiguamiento

Determine la relación de amortiguamiento ζ a partir del decremento logarítmico (amplitudes de pico sucesivas) o del método de ancho de banda de media potencia. Admite promediado de múltiples ciclos.

Decremento logarítmicoAncho de banda de media potenciaCálculo Automático

Método

Amplitud de pico x₁

Amplitud de pico x₂ (después de n ciclos)

Número de ciclos n (entre x₁ y x₂)

Preajustes rápidos

Resultados

Relación de amortiguamiento ζ

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Amortiguamiento (%)

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Decremento logarítmico δ / Ancho de banda Δf

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Factor de calidad Q

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Clasificación del amortiguamiento

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Método de decremento logarítmico

Método de ancho de banda de media potencia

Factor de calidad

Ejemplo — Decremento logarítmico

Datos: x₁ = 10 mm, x₂ = 6 mm, n = 1 ciclo

δ = (1/1) × ln(10/6) = ln(1.667) = 0.5108

ζ = 0.5108 / √(4π² + 0.5108²) = 0.5108 / 6.304 = 0.0811 (8.11%)

⚠️ Nota: La aproximación de decremento logarítmico ζ ≈ δ/(2π) es precisa con un margen de 1% para ζ < 0.1. Para mayor amortiguamiento, utilice la fórmula exacta.