Modal analysis

Summary

Modal analysis is the study of a vibrating structure through its normal modes: its natural frequencies, mode shapes and damping. Mathematically, it changes coordinates to the mode shapes, so that the coupled equations $M \ddot x + K x = f(t)$ split into independent equations for single oscillators. It is done numerically, with finite element models, or experimentally, from measured responses. Engineers use it to keep natural frequencies of buildings, bridges, vehicles and machines away from the frequencies of the loads they meet. See the definition.