Engine vs formula: Relative difference 5.2 × 10−4 %
f1: Engine 17.4533 / Classical method 17.4533 Hz · 6.4 × 10−6 %
f2: Engine 69.8132 / Classical method 69.8132 Hz · 1 × 10−4 %
f3: Engine 157.08 / Classical method 157.08 Hz · 5.2 × 10−4 %
Open in Stabileo ↗Sparse Cholesky solver (96 free DOFs)
Residual 0.00e0 (96 free DOFs)
Closed form / Classical method
fn = βn²/(2πL²) √(EI/μ); βsimple = nπ; βcantilever = 1.875104, 4.694091, 7.854757; βfixed = 4.730041, 7.853205, 10.995608
Assumptions
Linear elastic, small displacements. Prismatic Euler–Bernoulli frame members; truss bars carry axial force only with ideal pin joints. Self-weight is excluded. No shear deformation, geometric nonlinearity or design checks.
Uniform translational mass, consistent element mass matrix, no damping or rotary inertia. First three transverse bending modes; axial modes excluded. Mode amplitudes are arbitrary. Exported material density represents the entered mass per length.
Technical details
Production Stabileo solver · planar Euler–Bernoulli frame elements.
32 elements per span. Diagram extrema are sampled. Influence lines use 101 positions plus the section and its two sides; axle extrema are sampled, not an exact optimization. Shear is evaluated immediately left of the section.
Total nodal DOFs: 99