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→ Resonant vibrationestablishedclaim record

   mechanical → mechanical · loss to thermal

   • a cantilever or seismic mass with natural frequency near the excitation

   solid

   refs [1] [2]
2. 02
   Resonant vibration —produces→ Mechanical stress or strainestablishedclaim record

   mechanical → mechanical

   • cyclic bending stress at the root of the cantilever

   solid

   refs [2]
3. 03
   Mechanical stress or strain —drives→ Elastic deformationestablishedclaim record

   mechanical → mechanical

   σ = E · ε · Young's modulus E [Pa]

   solid

   refs [3]
4. 04
   Elastic deformation —produces→ Elastic stressestablishedclaim record

   mechanical → mechanical

   refs [3]
5. 05
   Elastic stress —drives→ Direct piezoelectric effectestablishedclaim record

   mechanical → electrical · loss to thermal

   • stress transmitted into a piezoelectric element

   solid · non-centrosymmetric crystal required

   refs [2]
6. 06
   Direct piezoelectric effect —produces→ Separated surface chargeestablishedclaim record

   electrical → electrical

   refs [3]
7. 07
   Separated surface charge —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes on the charged surfaces connected through a load

   refs [4]

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 · 4

1. [1]
   S. Roundy, P. K. Wright, J. Rabaey. A study of low level vibrations as a power source for wireless sensor nodes (2003)

   Computer Communications 26, 1131–1144 · doi:10.1016/S0140-3664(02)00248-7 · crossref ✓ 2026-09-19 · record
2. [2]
   A. Erturk, D. J. Inman. Piezoelectric Energy Harvesting (2011)

   Wiley · doi:10.1002/9781119991151 · crossref ✓ 2026-09-19 · record
3. [3]
   J. F. Nye. Physical Properties of Crystals: Their Representation by Tensors and Matrices (1985)

   Oxford University Press · book, no DOI · record
4. [4]
   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