Sommerfeld effect¶

Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics.

Version: v1 · 2026-09-28 · History
Domain-specific #: 12164
Domain group: Natural Sciences
Origin domain: Physics
Subdomains: Nonlinear Mechanics, Nonlinear Vibrations → Physics

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 system pass through resonance and jump to a higher-speed, lower-vibration regime.

The defining relation is reciprocal energy exchange between the drive and a compliant structure. Treating the motor speed as a prescribed input misses the effect; speed must be a dynamical variable coupled to structural motion and motor torque–speed behavior. Nonlinearity can create multiple coexisting attractors, hysteresis, and dependence on startup conditions. A routine startup may enter the resonant capture state even when another stable trajectory at the same parameters corresponds to successful passage. Related behavior appears in machines on flexible foundations, rotor systems, and drilling models with torsional vibration.

The effect is not ordinary resonance under a fixed-frequency external force. In ordinary resonance the forcing frequency is imposed; here the oscillator's response changes the source's speed and allocation of power. Nor does every vibration-induced efficiency loss constitute a Sommerfeld effect. The characteristic signature is resonance capture: added drive energy goes mainly into vibration, speed increases little, and eventual escape produces a discontinuous or rapid speed transition. The abstraction is the feedback-mediated redistribution of drive energy in a coupled nonideal source–oscillator system.

Structural Signature¶

Sig role-phrases:

the nonideal drive — motor or rotor whose speed responds dynamically to load rather than remaining externally prescribed
the rotating imbalance — periodic forcing generated as the drive turns
the compliant support — structure with a natural vibration frequency accessible during acceleration
the resonance approach — rotor speed bringing the forcing frequency near the structural mode
the reciprocal load feedback — growing structural motion increasing resisting torque on the drive
the energy-capture plateau — added input power flowing mainly into vibration while rotational speed remains near resonance
the multistable regime — coexisting captured and passed-through attractors with outcome dependent on startup or perturbation
the escape threshold — sufficient power or disturbance producing rapid transition through resonance
the post-resonance branch — higher speed with lower vibration after capture ends
the fixed-force boundary — distinction from ordinary resonance whose excitation frequency is imposed independently of response

What It Is Not¶

Not ordinary resonance under prescribed forcing frequency. Rotor speed is a dynamical variable altered by structural vibration rather than an externally fixed input.
Not every vibration-related efficiency loss. The signature is resonance capture: more drive feeds oscillation while rotational speed remains near the structural natural frequency.
Not a one-way motor-to-structure effect. The support motion changes the torque demand and feeds back on the unbalanced rotor.
Not necessarily a smooth speed response. Multiple attractors and hysteresis can produce abrupt escape to a higher-speed, lower-vibration branch.
Not determined by input power alone. Startup path, perturbations, torque–speed behavior, damping, imbalance, and initial conditions influence capture.
Not visible in a model with imposed rotor speed. The source–oscillator coupling and energy allocation must be represented explicitly.
Not a permanent speed limit. Sufficient power or a state-changing perturbation can carry the system through resonance and end the capture.

Scope of Application¶

The Sommerfeld effect applies to nonideal motor–structure systems where rotor speed evolves dynamically and unbalance-driven structural resonance feeds back on motor torque and energy allocation.

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.
Vibration isolation and control. Mitigation changes damping, stiffness, imbalance, control, or ramp trajectory to avoid or cross capture safely.
Experimental diagnosis. Speed, drive power, torque, and structural response must jointly show where energy is diverted.
Applicability boundary. Ordinary fixed-frequency resonance, a speed plateau alone, and generic vibration loss are insufficient; prescribed-speed models cannot reproduce the defining feedback.

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. The sharper diagnostic question is whether torque–speed and structural response interact strongly enough to create a stalled branch, hysteresis, and sudden transition as drive power changes.

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. This representation also predicts which changes—reduced imbalance, altered stiffness or damping, or greater torque margin—shrink the capture region and permit safer resonance passage.

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. Ordinary passage through resonance under prescribed speed lacks the defining reciprocal speed–vibration feedback.

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. A stalled project or economic plateau is only metaphor; the named effect requires a driven rotor coupled to a resonant mechanical system.

Examples¶

Canonical¶

An unbalanced motor mounted on a flexible support is slowly driven toward the support's natural frequency. Instead of speed rising smoothly with increased motor power, vibration amplitude grows and the motor can linger near resonance. The rotating imbalance feeds the support; the support's motion changes the load experienced by the motor, and input energy is captured in structural oscillation. Once drive torque exceeds a threshold, the system may jump to a higher-speed branch beyond resonance. Different stable responses can coexist, so acceleration and deceleration can follow different paths. A rigidly prescribed rotating force lacks the reciprocal motor–support feedback and does not instantiate the full Sommerfeld effect.

Mapped back: The motor is the nonideal drive with rotating imbalance on the compliant support. Approaching resonance creates the reciprocal load feedback and energy-capture plateau, with multistable regime, escape threshold, and post-resonance branch.

Applied / In Practice¶

During run-up of rotating machinery on a flexible test stand, engineers measure shaft speed, motor current, support acceleration, and phase. A plateau in speed accompanied by rising vibration suggests energy capture near a structural mode. They test the diagnosis by changing support stiffness, imbalance, ramp rate, or available torque and comparing the shift in capture and escape. Controls can avoid dwelling near resonance or supply enough torque to cross it rapidly, while redesign may isolate or stiffen the support. The response is not diagnosed from vibration alone; rubbing, control limits, or electrical saturation are competing explanations.

Mapped back: Measurements trace the resonance approach, reciprocal load feedback, and energy-capture plateau. Stiffness and imbalance perturbations target the compliant support and rotating imbalance; torque tests the escape threshold, while competing diagnoses enforce the fixed-force boundary separating forced resonance from the coupled effect.

Structural Tensions¶

T1 — Identity versus admissible variation. Sommerfeld effect must remain recognizable across legitimate variants. Admissible variation is bounded by this condition: Motor and support dynamics can capture speed near a structural natural frequency during startup. The stable element is expressed by this invariant: Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics. Treating every surface change as a new abstraction fragments the identity, while allowing a change to the constitutive relation produces a false positive.

Diagnostic: After the proposed variation, can an analyst still establish this invariant: Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics?

T2 — Recognition versus proxy. The domain needs observable or inferential evidence for Sommerfeld effect, but the evidence is not automatically the identity. The working recognition rule is: the fixed-force boundary — distinction from ordinary resonance whose excitation frequency is imposed independently of response. A familiar indicator can occur without the defining relation, and the relation can persist when a customary detector is unavailable.

Diagnostic: Does the evidence establish the defining claim—Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics—or only a correlated sign?

T3 — Definition versus operational judgment. A compact definition aids reuse, whereas actual classification in nonlinear mechanics can require expert decisions about boundary conditions, measurements, conventions, or exceptions. The defining relation is reciprocal energy exchange between the drive and a compliant structure. The definition must constrain those judgments without pretending that every admissible case can be recognized from a label alone.

Diagnostic: Which observation would make a competent practitioner reject the classification under the stated definition?

T4 — Scope versus overextension. Sommerfeld effect has a genuine habitat in which motor and support dynamics can capture speed near a structural natural frequency during startup. Yet Ordinary fixed-frequency resonance, a speed plateau alone, and generic vibration loss are insufficient; prescribed-speed models cannot reproduce the defining feedback. A useful application map therefore has to be broad enough to cover recurring practice and narrow enough to exclude merely topical or metaphorical occurrences.

Diagnostic: Can the claimed application fill the same carrier and relation roles, or has only the name traveled?

T5 — Transfer versus domain accent. Knowledge about Sommerfeld effect can travel within its home domain, and some structural lessons may travel farther. 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. What transfers must be separated from the specialist vocabulary, warrant, and closure conditions that remain anchored in nonlinear mechanics.

Diagnostic: Is the receiving case a literal instance of Sommerfeld effect, a co-instance of Resonance, or only an analogy?

T6 — Autonomy versus reduction. Sommerfeld effect is a strict specialization of Resonance, but the edge does not erase the domain differentia. The broader node supplies only the necessary structural relation; nonlinear mechanics supplies the carrier, warrant, boundary, and exception conditions expressed by this identity: Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics. The entry is over-split if those conditions add no discriminating work and under-specified if the parent alone is used for cases that require them.

Diagnostic: Can a domain expert use the added conditions to distinguish Sommerfeld effect from another case that equally instantiates Resonance?

Structural–Framed Character¶

Sommerfeld effect is mixed: structurally specifiable but materially dependent on its disciplinary frame. Its structural side consists of the carrier the nonideal drive — motor or rotor whose speed responds dynamically to load rather than remaining externally prescribed and the constitutive relation Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics. Its framed side comes from nonlinear mechanics, which fixes what the terms denote, what counts as evidence, and when a qualification or exception defeats the classification.

Across the principal tests, the entry is not merely a free-floating pattern. Evaluative weight: the identity can be stated descriptively even when its use has practical or normative consequences. Practice dependence: the fixed-force boundary — distinction from ordinary resonance whose excitation frequency is imposed independently of response. Institutional stabilization: disciplinary conventions may stabilize the name and test without necessarily creating every underlying event or relation. Vocabulary portability: the invariant is Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics. Import versus recognition: an outside case qualifies literally only if the same typed roles and collapse condition are available; otherwise the comparison is analogical.

The reusable remainder is Resonance under a reviewed subsumption relation. That node preserves the necessary cross-domain organization after the nonlinear mechanics-specific carrier, evidence, and exceptions are removed. Sommerfeld effect remains autonomous because its recognition and collapse conditions distinguish cases that the parent alone leaves together.

Structural Core vs. Domain Accent¶

What is skeletal. The portable skeleton is a typed carrier organized by a constitutive relation, an invariant, a recognition test, and a collapse condition. Here the carrier is the nonideal drive — motor or rotor whose speed responds dynamically to load rather than remaining externally prescribed. The decisive relation is Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics, which also states the controlling invariant at this level. Stripped of specialist nouns, this organization is represented by Resonance.

What is domain-bound. nonlinear mechanics supplies the actual objects or agents, admissible transformations, units or conventions, standards of warrant, and named exceptions. In this case, recognition requires evidence for the fixed-force boundary — distinction from ordinary resonance whose excitation frequency is imposed independently of response. Admissible variation is bounded by the condition that motor and support dynamics can capture speed near a structural natural frequency during startup, and the classification collapses when rotor speed is a dynamical variable altered by structural vibration rather than an externally fixed input. These are constitutive differentia, not illustrative decoration.

Why it remains a domain-specific node. The reviewed DAG relation is subsumption to Resonance. Outside nonlinear mechanics, the parent captures only the reusable structural remainder. The specialist name remains literal only where the fixed-force boundary — distinction from ordinary resonance whose excitation frequency is imposed independently of response can be established under the domain's standards of warrant.

This entry is a kind of Resonance.

Immediate parent — Resonance (subsumption). Sommerfeld effect is a domain-specific kind of Resonance: Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics. The parent supplies the necessary broader identity—Amplified response at frequency.—while the candidate adds the source-domain carrier, recognition rule, and failure conditions. The defining source account begins: 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.
Nearest catalog surface declined — Aharonov–Casher effect. Its rematch score was 0.183456. Retrieval proximity did not establish synonymy or parentage; the carrier, invariant, and collapse condition remain different.
Related reasoning operations. Evidence, comparison, boundary testing, and representation can support a case without becoming additional DAG parents.

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

Show alternative paths (9)

Neighborhood in Abstraction Space¶

Sommerfeld effect sits in a sparse region of the domain-specific corpus (80^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Resonance. This is the reviewed immediate parent or structural prerequisite, not a synonym. Tell: retain Sommerfeld effect only when the domain-specific relation Sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics. and its source-domain warrant are established; otherwise route the case to Resonance.
Wolf Tone. This is the closest catalog retrieval surface, not an accepted synonym or parent. Tell: Ask which entry's carrier, invariant, and collapse test the case actually satisfies; shared vocabulary or a score of 0.679416 is insufficient.
Not ordinary resonance under prescribed forcing frequency. Rotor speed is a dynamical variable altered by structural vibration rather than an externally fixed input. Tell: Require the positive recognition condition that the fixed-force boundary — distinction from ordinary resonance whose excitation frequency is imposed independently of response.
Not every vibration-related efficiency loss. The signature is resonance capture: more drive feeds oscillation while rotational speed remains near the structural natural frequency. Tell: Replace the familiar surface feature and test whether sommerfeld effect denotes mechanical phenomenon within nonlinear mechanics.
A detector, representation, or consequence. A method may reveal Sommerfeld effect, a notation may describe it, and an outcome may follow from it without any of those being identical to the abstraction. Tell: Would the defining relation remain if the present detector, notation, or downstream effect changed?
A metaphorical transfer. A case outside the home domain may resemble the structure while lacking its native role types and standards of warrant. Tell: If only the general organization survives, route the comparison to Resonance rather than treating it as another Sommerfeld effect instance.

References¶

Frozen Wikipedia revision: https://en.wikipedia.org/wiki/Sommerfeld_effect (revision 1315828813).
DOI: https://doi.org/10.1016/j.ifacol.2016.07.975
DOI: https://doi.org/10.1016/j.physrep.2016.05.002
DOI: https://doi.org/10.1007/s11071-014-1292-6
Supporting reference preserved in the packet: https://jyx.jyu.fi/bitstream/123456789/51180/1/1s2.0s2405896316312630main.pdf
Supporting reference preserved in the packet: https://jyx.jyu.fi/bitstream/123456789/50751/1/1s2.0s0370157316300928main.pdf

The frozen Wikipedia revision is discovery provenance. The cited source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; URL transport failure alone was not treated as substantive contradiction.