Mechanical vibration → Electrical work

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.09 × C.15 · Mechanical vibration × Magnetostrictivefamily: MagnetostrictiveD.09 × C.14 · Mechanical vibration × Electromagnetic inductionfamily: Electromagnetic induction

Typed bounds on this route

Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).

• Onsager–Casimir reciprocity · constitutive-relation · listed, never decisive
  L_ij(B) = ε_i ε_j L_ji(−B): the cross-coefficients of coupled linear transport are equal up to the time-reversal parities ε of the variables and reversal of the magnetic field; L_ij = L_ji is the zero-field, even-parity case

Steps

1. 01
   Mechanical vibration —drives→ Elastic deformationestablishedclaim record

   mechanical → mechanical · loss to thermal

   • cyclic deformation of an elastic member (a cantilever
   • a plate
   • a sheet) by base or inertial excitation; operation at a structural resonance amplifies the deformation but is not required

   solid

   refs [1] [2] [3]
2. 02
   Elastic deformation —produces→ Elastic stressestablishedclaim record

   mechanical → mechanical

   refs [4]
3. 03
   Elastic stress —drives→ Villari effectestablishedclaim record

   mechanical → magnetic · loss to thermal

   solid · ferromagnet required

   refs [5] [6]
4. 04
   Villari effect —produces→ Changing magnetic fluxestablishedclaim record

   magnetic → magnetic

   refs [5] [6]
5. 05
   Changing magnetic flux —drives→ Electromagnetic inductionestablishedclaim record

   magnetic → electrical · loss to thermal

   ℰ = −dΦ/dt · rate of change [1/s]

   • the changing flux threads a conducting loop

   conductor required

   refs [7] [6]
6. 06
   Electromagnetic induction —produces→ Charge carriersestablishedclaim record

   electrical → electrical · loss to thermal

   refs [7] [6]
7. 07
   Charge carriers —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • carriers driven through an external load at the potential difference the source maintains

   refs [8]

Evidence for the complete composition · 0

No source on record for this exact composition. The sources below support the individual steps, not the route as a whole.

Evidence for the constituent relations · 8

1. [1]
   A. Erturk, D. J. Inman. Piezoelectric Energy Harvesting (2011)

   Wiley · doi:10.1002/9781119991151 · crossref ✓ 2026-09-19 · record
2. [2]
   S. Yang et al.. Performance enhancement of flexoelectric energy harvester by structural design (2025)

   International Journal of Smart and Nano Materials 16(4), 908–928 · doi:10.1080/19475411.2025.2592544 · record
3. [3]
   A. Kumar et al.. Vibration induced refrigeration using ferroelectric materials (2019)

   Scientific Reports 9, 3922 · doi:10.1038/s41598-019-40159-8 · record
4. [4]
   J. F. Nye. Physical Properties of Crystals: Their Representation by Tensors and Matrices (1985)

   Oxford University Press · book, no DOI · record
5. [5]
   L. Wang, F. G. Yuan. Vibration energy harvesting by magnetostrictive material (2008)

   Smart Materials and Structures 17, 045009 · doi:10.1088/0964-1726/17/4/045009 · crossref ✓ 2026-09-19 · record
6. [6]
   L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii. Electrodynamics of Continuous Media (Course of Theoretical Physics, Vol. 8, 2nd ed.) (1984)

   Pergamon · book, no DOI · record
7. [7]
   M. Faraday. Experimental researches in electricity (1832)

   Philosophical Transactions of the Royal Society 122, 125–162 · doi:10.1098/rstl.1832.0006 · crossref ✓ 2026-09-19 · record
8. [8]
   N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)

   Holt, Rinehart and Winston · book, no DOI · record