{
  "case": "modal_analysis / cantilever beam natural frequencies",
  "geometry": {
    "L_m": 2.0,
    "cross_section_m": [
      0.1,
      0.0125
    ]
  },
  "material": {
    "E_Pa": 210000000000.0,
    "nu": 0.3,
    "rho_kg_m3": 7850.0
  },
  "analytical_hz": [
    2.610978026691079,
    16.362852813641133,
    45.816785111669034
  ],
  "n_modes_compared": 2,
  "mesh_convergence": [
    {
      "size_factor": 2.0,
      "all_frequencies_hz": [
        2.685089618194626,
        18.14626897875392,
        21.32617877115344,
        58.679302489558104
      ],
      "compared_frequencies_hz": [
        2.685089618194626,
        18.14626897875392
      ],
      "analytical_hz": [
        2.610978026691079,
        16.362852813641133
      ],
      "error_pct": [
        2.8384609424488234,
        10.899176234268973
      ],
      "elapsed_s": 8.719975471496582
    },
    {
      "size_factor": 1.5,
      "all_frequencies_hz": [
        2.6578760620650788,
        17.198625216995325,
        21.125629360585524,
        51.04021420481293,
        99.95178524815908
      ],
      "compared_frequencies_hz": [
        2.6578760620650788,
        17.198625216995325
      ],
      "analytical_hz": [
        2.610978026691079,
        16.362852813641133
      ],
      "error_pct": [
        1.7961865207052021,
        5.107742597656549
      ],
      "elapsed_s": 34.58253860473633
    },
    {
      "size_factor": 1.0,
      "all_frequencies_hz": [
        2.641999523645591,
        16.785029720339267,
        21.018606352578495,
        48.178395967502034,
        97.99613429690835,
        98.42833512746661
      ],
      "compared_frequencies_hz": [
        2.641999523645591,
        16.785029720339267
      ],
      "analytical_hz": [
        2.610978026691079,
        16.362852813641133
      ],
      "error_pct": [
        1.1881178867608495,
        2.5800935295719323
      ],
      "elapsed_s": 196.94609832763672
    }
  ],
  "final_error_pct": [
    1.1881178867608495,
    2.5800935295719323
  ],
  "pass": true
}