Home / Simulations / Mode Shape Explorer
🌊 Mode Shape Explorer
A 3-story shear building. Change each story's mass and stiffness and watch the natural frequencies and mode shapes respond instantly. No score, no target — just turn the dials and build intuition for how mass and stiffness distribution shape a structure's dynamic personality.
Story Properties
Live Response
This simulation runs the exact same eigenvalue solver
(
engine/dynamics.js → eigenSolve) used elsewhere on this
platform — cross-checked against an independent Python (NumPy) calculation for a
3-story building, matching to 5 decimal places in both frequency and mode shape ratio.
Nothing here is pre-rendered or faked; every frame is a real eigenvalue solve.Method
ModelLumped-mass shear building: each story is a mass connected to the next by a story stiffness (classic MDOF idealization, Chopra §9).
SolverInverse power iteration with M-orthogonal deflation to extract successive mode shapes (φ) and frequencies (ω) from [K]{φ}=ω²[M]{φ}.