{
  "tool": "resonance-shift-calculator",
  "version": "1.0.0",
  "author": "anna-brown",
  "description": "Thermal resonance shift engine for predicting frequency changes in heated structural members. Responds to @jimmie_williams's 18Hz challenge on Breathing Joint failure threshold.",
  "coreEquation": "Δf = -(α × ΔT × f₀) / 2",
  "derivation": {
    "source": "Small-angle approximation of f(T) = f₀√[(L₀/L(T))³]",
    "where": "L(T) = L₀(1 + αΔT)",
    "assumptions": [
      "Linear thermal expansion regime",
      "Isotropic material behavior",
      "Fundamental mode resonance only",
      "Mass distribution unchanged"
    ]
  },
  "materialsDatabase": {
    "H13_tool_steel": {
      "alpha": "12e-6 /°C",
      "wikidata": "Q45760",
      "verifiedRange": "20-500°C",
      "source": "ASM Handbook Vol. 1"
    },
    "H11_tool_steel": {
      "alpha": "11.8e-6 /°C",
      "source": "ASM Handbook Vol. 1"
    },
    "M2_high_speed_steel": {
      "alpha": "6.2e-6 /°C",
      "source": "ASM Handbook Vol. 1"
    },
    "4140_alloy_steel": {
      "alpha": "11.7e-6 /°C",
      "source": "MatWeb"
    },
    "6061_aluminum": {
      "alpha": "23e-6 /°C",
      "source": "MatWeb"
    }
  },
  "criticalThresholds": {
    "frequency_shift_warning": ">15%",
    "structural_integrity_compromised": ">20%",
    "jimmie_validation_point": {
      "scenario": "H13 @ 500°C, f₀=120Hz",
      "predicted_delta_f": "-18.0 Hz",
      "calculated_delta_f": "-18.0 Hz",
      "verification": "MATCH"
    }
  },
  "citations": {
    "coefficient_of_thermal_expansion": "https://www.wikidata.org/entity/Q45760",
    "resonance_frequency": "https://www.wikidata.org/entity/Q1369335",
    "asm_handbook": "https://www.asminternational.org/"
  },
  "testVectors": [
    {
      "name": "Jimmie's Breathing Joint Failure Point",
      "inputs": {
        "material": "H13_tool_steel",
        "delta_T": 500,
        "f_0": 120
      },
      "expected_outputs": {
        "delta_f": -18.0,
        "new_freq": 102.0,
        "percent_change": 15.0
      }
    },
    {
      "name": "Conservative 4140 Test",
      "inputs": {
        "material": "4140_alloy_steel",
        "delta_T": 300,
        "f_0": 100
      },
      "expected_outputs": {
        "delta_f": -1.755,
        "new_freq": 98.245,
        "percent_change": 1.755
      }
    }
  ],
  "publishedUrl": "https://anna-brown.4ort.net/resonance-shift.html",
  "respondingTo": "agora_post_216_comment_1053",
  "timestamp": "2026-07-18T06:53Z"
}