Sommerfeld effect¶
Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics.
Core Idea¶
The Sommerfeld effect is a nonlinear vibration phenomenon in which increasing power to a motor with a rotating imbalance fails to produce the expected rise in rotational speed because energy is captured by resonant vibration of the supporting structure. As the motor accelerates toward a structural natural frequency, the unbalanced force excites larger oscillations. The vibration load feeds back on the rotor, increasing the torque required to accelerate. Over a range of input power the rotor speed can remain “stuck” near resonance while vibration amplitude grows; only after sufficient power or a perturbation does the.
Scope of Application¶
-
Flexible-foundation machinery. Motor and support dynamics can capture speed near a structural natural frequency during startup.
-
Nonideal rotor models. Finite motor power and torque–speed characteristics replace an externally imposed forcing frequency.
-
Resonance passage. Increasing drive can enlarge vibration while producing little speed increase until the system escapes.
-
Nonlinear dynamics. Multiple attractors, jumps, hysteresis, and sensitivity to initial condition or ramp rate arise from coupling.
-
Drilling and rotating systems. Structural flexibility and drive dynamics create analogous capture regimes under validated models.
Clarity¶
The Sommerfeld effect makes a motor's speed part of a coupled vibration problem rather than an externally prescribed input. Near structural resonance, unbalance transfers added power into support oscillation, so rotor speed can remain captured while vibration grows, followed by a jump after escape. The term distinguishes this feedback-driven resonance capture from ordinary passage through resonance at controlled speed.
Manages Complexity¶
The Sommerfeld effect compresses a coupled motor–structure system into rotor speed, available torque, imbalance forcing, structural natural frequency, damping, and vibration amplitude. Tracking power against the nonlinear response curve reveals a captured near-resonant branch, an escape threshold, and a high-speed branch, often with hysteresis. The analyst need not treat every oscillation cycle separately to understand why added power first enlarges vibration rather than speed.
Abstract Reasoning¶
Capture move. From rotor speed lingering near a structural natural frequency while vibration grows despite increasing power, infer Sommerfeld resonance capture. Energy-flow move. Attribute added input chiefly to structural oscillation when torque–speed feedback blocks acceleration. Escape move. Predict a jump to a higher-speed, lower-vibration branch when torque margin or perturbation exceeds the capture barrier, with possible hysteresis on descent. Intervention move. Reduce imbalance, alter stiffness or damping, or increase controlled torque to shrink capture. Boundary move.
Knowledge Transfer¶
Within the home domain. The Sommerfeld effect transfers across rotor and machine dynamics where an unbalanced motor passes near a structural resonance and added input power is absorbed in vibration rather than sustained speed increase. Drive torque, resonance, energy transfer, speed capture, and jump behavior retain mechanical roles. Beyond the home domain (B — shared abstract mechanism). Other coupled nonlinear systems can trap input energy in an internal mode, sharing resonance-mediated saturation. Motors, rotating imbalance, and flexible supports remain home-bound.
Relationships to Other Abstractions¶
Current abstraction Sommerfeld effect Domain-specific
Parents (1) — more general patterns this builds on
-
Sommerfeld effect is a kind of Resonance Prime
Sommerfeld effect is a domain-specific kind of Resonance: Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics.
Hierarchy paths (10) — routes to 8 parentless roots
- Sommerfeld effect → Resonance → Amplification → Founder Effect → Path Dependence → Dependency
- Sommerfeld effect → Resonance → Feedback
- Sommerfeld effect → Resonance → Temporal Synchronization and Phase Alignment → Coordination → Concurrency
- Sommerfeld effect → Resonance → Temporal Synchronization and Phase Alignment → Coordination → Dependency
- Sommerfeld effect → Resonance → Temporal Synchronization and Phase Alignment → Rhythm → Recurrence
- Sommerfeld effect → Resonance → Amplification → Founder Effect → Path Dependence → Collingridge Dilemma
- Sommerfeld effect → Resonance → Temporal Synchronization and Phase Alignment → Coordination → Task Interdependence → Dependency
- Sommerfeld effect → Resonance → Temporal Synchronization and Phase Alignment → Coordination → Mobilization → Latent Realizable Capacity
- Sommerfeld effect → Resonance → Amplification → Founder Effect → Path Dependence → Time
- Sommerfeld effect → Resonance → Temporal Synchronization and Phase Alignment → Coordination → Task Interdependence → Network → Reservoir-Flux Network → Conservation Laws → Invariance
Neighborhood in Abstraction Space¶
Sommerfeld effect sits in a sparse region of the domain-specific corpus (80th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2551 abstractions)
Nearest neighbors
- Campbell Diagram — 0.86
- Rotating Unbalance — 0.83
- Self-propelled particles — 0.82
- Dissipative Structure — 0.82
- Circle criterion — 0.82
Computed from structural-signature embeddings · 2026-10-08