Coulomb damping¶

Model mechanical energy loss by an approximately constant-magnitude dry-friction force opposing sliding velocity and producing piecewise motion with possible sticking.

Version: v2 · 2026-09-19 · History
Domain-specific #: 1570
Domain group: Applied Sciences & Engineering
Origin domain: Engineering & Design (beyond software)
Subdomains: Mechanical Engineering, Dry Friction Vibration → Engineering & Design (beyond software)
Aliases: Dry-friction damping, Constant-friction damping

Core Idea¶

Coulomb damping is vibration attenuation produced by sliding dry friction idealized as a force of nearly constant magnitude \(F_c=\mu N\) directed opposite instantaneous velocity. For a single-degree-of-freedom oscillator the moving phases may be written \(m\ddot x+kx=-F_c\,\operatorname{sgn}(\dot x)\), with separate conditions at zero velocity. The force law is discontinuous and motion is solved piecewise between reversals.

During each sliding half-cycle, friction removes work equal to its magnitude times distance traveled. Under the ideal constant-force, linear-spring model, successive peak amplitudes decrease by an approximately constant amount rather than the exponential envelope characteristic of viscous damping.

How would you explain it like I'm…

Rubbing Slows the Swing

Push a toy on a spring across a rough table and let go. It bounces back and forth, but the rubbing on the table slows it down. Each swing gets shorter by about the same amount, and at the end the toy may stop a little off from the middle because the rubbing holds it still.

Dry-Friction Slowdown

Coulomb damping is how sliding, dry rubbing slows down something that is shaking back and forth, like a block on a spring sliding on a rough floor. The rubbing force is about the same size all the time and always pushes against the direction the block is moving. Every time the block slides, the rubbing takes away some of its energy. In the simple model, each swing is shorter than the last by roughly the same amount, instead of shrinking by a fraction like with oil or air drag. Near the end, the rubbing can grab the block and stop it before it gets back to the exact middle.

Dry-Friction Vibration Damping

Coulomb damping is the loss of vibration energy caused by dry sliding friction, modeled as a force of nearly constant size, F = mu N (friction coefficient times normal force), always opposite to the velocity. For a mass on a spring, the motion is solved in pieces, one sliding stroke at a time, because the friction force flips direction whenever the velocity changes sign. In each stroke, friction does work equal to its size times the distance slid. In the ideal model, peak amplitude drops by about the same amount every half-cycle, a straight-line decay, unlike viscous damping, where amplitude shrinks by a constant fraction (exponential decay). Eventually static friction can hold the mass still before the spring pulls it back to the true equilibrium, so it may stop anywhere in a small 'sticking band'. This is an idealization; real friction can depend on speed, surface condition and load.

Coulomb damping is vibration attenuation from sliding dry friction, idealized as a force of nearly constant magnitude F_c = μN acting opposite to the instantaneous velocity. For a single-degree-of-freedom oscillator the sliding phases obey m x'' + k x = -F_c sgn(x'), with separate conditions when the velocity is zero. The force law is discontinuous, so the motion is solved piecewise between velocity reversals. In each sliding half-cycle friction does work equal to F_c times the distance traveled, which, with a linear spring and constant friction, produces an approximately constant decrement in successive peak amplitudes rather than the exponential decay envelope of viscous damping. As energy runs out, static friction can arrest the mass before it returns to nominal equilibrium, so the final rest position lies somewhere in a sticking band. The model is an idealization: breakaway force, velocity dependence, surface condition, varying normal load, Stribeck effects and microslip can all break the constant-magnitude assumption. An equivalent viscous damper can match energy loss at one amplitude and frequency but does not reproduce the piecewise waveform or the constant decrement.

Scope of Application¶

The abstraction is literal wherever practitioners can identify the same constitutive roles, apply the same boundary tests, and obtain the same kind of output. The following habitats are uses of Coulomb damping itself, not metaphors based only on resemblance.

Vibration analysis. Predicting free-decay envelopes under sliding friction.
Mechanical joints. Approximating dissipation where interfaces undergo gross slip.
Isolation devices. Comparing frictional and viscous attenuation models.
Parameter estimation. Inferring effective friction magnitude from peak decrement.
Simulation. Handling sign changes and stick conditions with event-aware dynamics.
Model validation. Checking amplitude and velocity dependence against observed decay.

Clarity¶

A clear account of Coulomb damping must preserve the recognition invariant stated in the Core Idea rather than rely on the title alone. State whether static and kinetic friction are distinguished. Declare the normal-load and constant-magnitude assumptions. Solve between velocity reversals rather than smoothing the sign change silently. Test the predicted constant peak decrement across more than one amplitude range. These declarations are not editorial extras: each changes what observations count, which transformations are licensed, and what conclusion can be drawn.

Manages Complexity¶

Coulomb damping manages complexity by replacing a diffuse field of observations or possible operations with a bounded role structure: sliding interface supplies contact between surfaces supplies dry-friction energy loss.; normal load supplies contact loading scales the ideal friction magnitude.; opposing force supplies force direction reverses with sliding velocity.; restoring dynamics supplies elastic and inertial terms produce oscillatory reversals.; piecewise phases supplies a fixed force sign applies between consecutive zero-velocity events..

Abstract Reasoning¶

Draw the free-body model and identify the sliding interface.
Estimate friction magnitude and direction for each moving phase.
Integrate the linear dynamics until the next zero-velocity event.
Update force sign or test the static-friction sticking condition.
Track frictional work and successive peak amplitudes.
Compare predictions against viscous and state-dependent friction alternatives.
Retain the law only over the range where its diagnostics hold.

Knowledge Transfer¶

The strict upward abstraction is Damping. Coulomb Damping instantiates Damping because dry-friction work irreversibly removes mechanical energy from motion. Within dry friction vibration, the full mechanism transfers literally when the same roles and boundary tests recur. Beyond that domain, only the parent-level skeleton should travel. Reusing the label Coulomb damping after removing its constitutive vocabulary would hide a change of mechanism behind an analogy. The honest transfer rule is therefore two-stage: recognize the domain-specific pattern first, then lift only the parent relation that remains invariant under a substrate change.

Relationships to Other Abstractions¶

Current abstraction Coulomb damping Domain-specific

Parents (1) — outgoing typed relations

Coulomb damping is a kind of Damping Prime

Coulomb Damping instantiates Damping because dry-friction work irreversibly removes mechanical energy from motion.

Hierarchy paths (2) — routes to 2 parentless roots

Coulomb damping → is a kind of Damping → is a kind of Dissipation → presupposes Irreversibility → is a kind of Reversibility and Irreversibility

Show alternative path (1)

Neighborhood in Abstraction Space¶

Coulomb damping sits in a sparse region of the domain-specific corpus (99^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2769 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25