Torsional Vibration Natural Frequency mechanism

Model scope

Core shaft-disk formula is standard under the stated idealized assumptions, but the specification needs the explicit fn=ωn/(2π) formula, required unit conventions, and the exact shaft boundary/model assumptions before it can receive PASS. The empty honest_label is inadequate; it should disclose the fixed-end, rigid-disk, massless-shaft, undamped single-degree-of-freedom assumptions.

• The listed formulas define kt and ωn but omit the formula for the declared output fn; the standard relation must be stated explicitly as fn=ωn/(2π).
• The model scope is not stated: these formulas assume a uniform, massless shaft fixed at one end with a rigid disk inertia J at the other, and negligible damping and shaft distributed inertia.
• Jp must mean the shaft Saint-Venant torsional constant. Calling it a polar second moment is valid directly for circular shafts, but not generally for noncircular sections.

Units and conventions

• Use G in Pa (N/m²), Jp in m⁴, and L in m; kt then has units N·m/rad, with radians treated as dimensionless.
• Use J as the disk mass moment of inertia in kg·m²; it must not be confused with the shaft torsional constant Jp.
• ωn is in rad/s and fn is in Hz, using fn=ωn/(2π).
• For noncircular shafts, Jp requires the appropriate Saint-Venant torsional constant rather than the ordinary geometric polar second moment.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "G_Pa": 80000000000,
    "Jp_m4": 1e-8,
    "L_m": 1,
    "J_disk_kg_m2": 0.02
  },
  "expected_outputs": {
    "kt_Nm_per_rad": 800,
    "omega_n_rad_per_s": 200,
    "fn_Hz": 31.83098862
  },
  "working": "kt=(G·Jp)/L=(80,000,000,000·0.00000001)/1=800 N·m/rad. ωn=√(kt/J)=√(800/0.02)=√40,000=200 rad/s. fn=ωn/(2π)=200/6.283185307=31.83098862 Hz."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification provides no stated domain-validation rules. L = 0 causes division by zero and must be rejected; negative stiffness inputs produce an undefined real square root. The formulas also do not define an actual piecewise branch at the sign switch.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json