Tools · Signal analysis
Damping converter
Damping comes in five different dialects depending on whether you measured it from a bump test, a ring-down or a frequency response. Enter any one and get the rest.
Ring-down tip: if the amplitude drops from A0 to An over n cycles, δ = ln(A0/An) / n.
The relationships
Q = 1 / 2ζ η = 2ζ (at resonance) δ = 2πζ / √(1 − ζ²)
Δf−3dB = 2ζ·fn = fn / Q
The half-power (−3 dB) bandwidth method is what you'd use on a measured frequency response or impact test. The log decrement is for a free-decay (ring-down) time signal. Q tells you how much a resonance amplifies a force at its natural frequency. All of these assume light, viscous damping, which is a good model for most steel structures and piping.
Method & sources
What it calculates
- Linear viscous damping relations: Q = 1/2ζ; η = 2ζ (equivalent at resonance); δ = 2πζ/√(1 − ζ²) (exact for viscous damping).
- Half-power (−3 dB) bandwidth Δf = 2ζ·fn; cycles to decay to 10% = ln(10)/δ.
Assumptions & limits
- The half-power method is accurate for light damping (ζ below about 0.1) and well-separated modes.
- Structural (hysteretic) damping is only equivalent to viscous damping at resonance.
Verified: ζ = 0.03 gives Q = 16.67, δ = 0.1886 and 3 Hz bandwidth at 50 Hz, checked by hand.