Equivalent Viscous Damping⚠ unverified
Physics / Vibration · Compute the equivalent viscous damping coefficient from a hysteresis loop
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| hysteresis_energy | hysteresisenergy | J | 1.0 | Energy dissipated per cycle (area of the hysteresis loop) |
| amplitude | amplitude | m | 1.0 | Displacement amplitude of the cycle |
| frequency | frequency | rad/s | 1.0 | Excitation frequency |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | ceq | N*s/m | Equivalent viscous damping coefficient, in newton-seconds per metre (N*s/m). Returns 0.0 if ``amplitude`` or ``frequency`` is non-positive |
The science & history
Understanding the Parameters
- $E_h$ — area of the force–displacement hysteresis loop.
- $X$, $\omega$ — operating amplitude and frequency (must match the loop measurement conditions).
- $c_{\mathrm{eq}}$ — linear viscous model that dissipates the same energy per cycle at that $X,\omega$.
Derivation (Approaching a Proof)
Viscous damper force $c\dot{x}$ on $x = X\sin\omega t$ dissipates $E = \oint c\dot{x}\,dx = \pi c\omega X^{2}$ per cycle. Set equal to measured $E_h$ ⇒ $c_{\mathrm{eq}} = E_h/(\pi\omega X^{2})$.
History
Equivalent viscous damping is the standard bridge from nonlinear/hysteretic damping to linear SDOF analysis.
Related Concepts: Damping Ratio, Logarithmic Decrement, Magnification Factor
Notes: Registry calculator equivalent-viscous-damping (unverified). Harmonic steady-state energy
match only.