Stiffened Fuselage Barrel Natural Flexural Vibrations
Modal Analysis (beam-shell)PASS · 1.63%First natural flexural vibration frequency of an aircraft fuselage barrel reinforced by 96 stringers and 15 frames: verified against a 1D Timoshenko beam model accounting for shear deformation, rotatory inertia, and distributed stringer mass.
- Tolerance:
- 5%
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Open & Solve in BrowserProblem statement
- Geometry
- Stiffened fuselage barrel R = 1.95 m, L = 7.0 m, t = 1.8 mm, 96 tee stringers and 15 frames. Total structural mass m = 815.00 kg (linear mass m' = 116.43 kg/m, EI = 4.239e9 N·m², GA_s = 5.95e8 N).
- Material
- Aviation aluminum: E = 72 GPa, ν = 0.33, ρ = 2780 kg/m³.
- Boundary conditions
- Cantilever root clamping at x = 0 (all 6 DOFs clamped along the root ring).
- Measured quantity
- First bending mode frequency f_1. Classical Euler-Bernoulli gives 68.91 Hz (unrealistic, ignores shear). 1D Timoshenko reference with shear flexibility and rotatory inertia: f_ref = 43.741 Hz. Native 3D beam-shell FE computation: f_FE = 43.029 Hz (degenerate Y/Z bending pair, 1.63% deviation).
WebCAE Terminal
Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:
units m
material E=72e9 nu=0.33 density=2780
frame up=z
frame patch geom=cyl o=0,0,0 axis=1,0,0 ref=0,0,1 r=1.95 a0=0 a1=360 len=7 nu=192 nv=56 t=0.0018
frame stiffen patch=1 i="0:191:2" section=tee d1=0.024 d2=0.036 d3=0.0016 d4=0.0016 flush=inner
frame stiffen patch=1 j="0:55:4" section=ibeam d1=0.09 d2=0.03 d3=0.002 d4=0.0025 flush=inner
frame support patch=1 side=i0 dofs=all
frame solve modal nmodes=8
frame probe frequency mode=1 id="f1"Results comparison
| Reference value | 43.741 Hz (f1 Timoshenko bending), 43.744 Hz (no diaphragm), 815.00 kg (mass) |
| Our result | 43.029 Hz (f1, 1.63%), 43.014 Hz (no diaphragm, 1.67%), 815.00 kg (0.00%) |
| Deviation | 1.63% |
| Tolerance | 5% |
| Status | PASS · 1.63% |
| Element family | Beam + Shell |
| Mesh details | 14208 shell quad + 8256 beam stiffeners (frame patch + frame stiffen), 14305 nodes, 85830 DOFs; webcae_solve |
Updated: 2026-10-19 · WebCAE solver