Harmonic response of cantilever beam (P2 Tet10)

Harmonic analysisPASS · 0.23%

Frequency response and resonant tip amplitude of a prismatic cantilever beam under harmonic tip transverse load, verified against Euler-Bernoulli analytical modal frequency and single-degree-of-freedom resonance peak amplitude.

Tolerance:: 5%

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Problem statement

Geometry: Prismatic cantilever beam: L = 200 mm, b = 20 mm, h = 20 mm, quadratic tetrahedral mesh (TET10).
Material: Structural steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³.
Boundary conditions: Fixed at root face (x = 0); harmonic transverse tip force F_z = -1000 N at free face (x = 200 mm).
Measured quantity: Fundamental bending resonance frequency f₁ (analytical: 407.7 Hz) and tip peak vibration amplitude under 5% modal damping (analytical: 9.707 mm).

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 mm
material E=200e9 nu=0.3 density=7850
primitive box dx=200 dy=20 dz=20
mesh tet size=8 order=2
fix surface number 1
load surface number 2 force=-1000 component=z
solve harmonic fmin=350 fmax=460 npoints=120 zeta=0.05 nmodes=5
probe harmonic_peak_frequency mode=1
probe harmonic_amplitude x=200 freq=406.8

Results comparison

Reference value	f₁ = 407.7 Hz, u_res = 9.707 mm
Our result	f₁ = 406.8 Hz, u_res = 9.627 mm
Deviation	0.23%
Tolerance	5%
Status	PASS · 0.23%
Element family	Solid element
Mesh details	P2 TET10 second-order mesh, 1485 elements, 2514 nodes

Updated: 2026-08-30 · before version numbering (before 0.1.1)