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.10 · Mechanical vibration × Piezoelectricfamily: Piezoelectric

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).

• Electromechanical coupling factor · formula-bound · hard, applies to this route
  converted fraction per cycle ≤ k² = d²/(s·ε)

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→ Direct piezoelectric effectestablishedclaim record

   mechanical → electrical · loss to thermal

   • stress transmitted into a piezoelectric element

   solid · non-centrosymmetric crystal required

   refs [1]
4. 04
   Direct piezoelectric effect —produces→ Separated surface chargeestablishedclaim record

   electrical → electrical

   refs [4]
5. 05
   Separated surface charge —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes on the charged surfaces connected through a load

   refs [5]

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 · 5

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]
   H. B. Radousky, H. Liang. Energy harvesting: an integrated view of materials, devices and applications (2012)

   Nanotechnology 23, 502001 · doi:10.1088/0957-4484/23/50/502001 · crossref ✓ 2026-09-19 · record