Physical units for M03-D
Dimensional equations and a numerical equivalence check; specimen calibration remains open.
A dimensional definition at one fixed geometry
dq/dt = v M dv/dt = F − Cv − K₀(1 + βm)q dm/dt = αE Cv²(1 − m) − m/τ
| Quantity | Unit | Meaning |
|---|---|---|
| q, v | m; m/s | Displacement and velocity |
| M | kg | Effective moving mass |
| K₀, C | N/m; N·s/m | Baseline stiffness and viscous coefficient |
| αE, τ | J⁻¹; s | Energy-to-state writing coefficient and recovery time |
| m, β | dimensionless | State and stiffness coupling |
Cv² is power, so αE Cv² is a rate. For β > 0 this is a stiffening law. No material calibration is claimed. Changing its sign to model softening defines a different hypothesis.
The unit conversion is checked
t* = √(M/K₀), q* = Q, F* = K₀Q c̄ = C/√(MK₀), ᾱ = αE K₀Q², τ̄ = τ/t*
The included synthetic example reproduces M03-D at normalized L=1. SI and normalized integrations agree within 4.1 × 10⁻¹¹. The model’s normalized L is not automatically a length in metres; geometry-dependent stiffness needs its own derivation or measurements.
Definition, energy ledger and calibration requirements · Numerical result · Blank calibration record
What the check does not establish
The cost and mechanism of changing stiffness remain absent from the subsystem energy ledger. Synthetic SI numbers do not identify a named elastomer. Parameters, state readout, noise and practical identifiability must be resolved on calibration data before a held-out material comparison.
Frequency ratios depend on recovery, saturation, strain rate and temperature. The often cited factors of 10 at matched cycles and 100 at matched duration are low-write, negligible-recovery limits under imposed displacement and constant damping.
Finite-retention sensitivity examples · Separate E02-F pilot