Nonlinear dynamics — Duffing Energy

Nonlinear dynamicsPASS · <0.01%

Transient nonlinear dynamics, impact, and conservation-law verification. Checks: nonlinear restoring force and conservative integration.

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Problem statement

Geometry: Undamped Duffing oscillator m=1, k=1, beta=1, x(0)=1, v(0)=0, no forcing.
Material: Constitutive or analytical definition: m xdd+kx+beta x^3=0 with exact Hamiltonian.
Boundary conditions: Required solver capability: nonlinear_transient_driver. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Total energy E=0.5*v^2+0.5*x^2+0.25*x^4=0.75 at every time; turning points remain x=+/-1.

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
dynamic oscillator duffing m=1 k=1 beta=1 x0=1 v0=0
solve transient method=verlet dt=0.001 t_end=20
extract energy_conservation

Reference value	E=0.750000 J, turning_points=+/-1.0000
Our result	E=0.750000 J, max_drift=4.38e-5%
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	Undamped Duffing oscillator m=1, k=1, beta=1, symplectic Verlet

Updated: 2026-10-27 · version not recorded