Longitudinal harmonic response of rod (P1 Tet4)
Harmonic analysisPASS · 0.03%Axial dynamic frequency response and resonance amplitude of a steel rod under longitudinal harmonic tensile force, verified against exact 1D continuous wave propagation velocity and analytical resonance amplification factor.
- Tolerance:
- 1%
- Reference:
- Closed-form theory
The target value is an exact analytical solution, computed from the formula stated below — not a number taken from another solver.
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Open & Solve in BrowserProblem statement
- Geometry
- Steel rod: L = 100 mm, b = 10 mm, h = 10 mm, linear tetrahedral mesh (TET4).
- Material
- Structural steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³.
- Boundary conditions
- Fixed at root face (x = 0); harmonic axial tensile force F_x = 1000 N at free face (x = 100 mm).
- Measured quantity
- Fundamental axial resonance frequency f_axial (analytical: c / (4L) = 12930.4 Hz) and tip peak vibration amplitude under 2% modal damping (analytical: 0.03860 mm).
Results comparison
| Reference value | f₁ = 12930.4 Hz, u_res = 0.03860 mm |
| Our result | f₁ = 12926.1 Hz, u_res = 0.03860 mm |
| Deviation | 0.03% |
| Tolerance | 1% |
| Status | PASS · 0.03% |
| Element family | Solid element |
| Mesh details | P1 TET4 first-order mesh, 346 elements, 164 nodes |
Updated: 2026-08-30 · WebCAE solver