1. Introduction

Based on a description of the geometry and materials of structures, the finite element method makes it possible to create a precise and reliable model but of large dimensions. In the case of a dynamics problem, we want to calculate the response of a system for different times (transient analysis) or for different frequencies (harmonic analysis). The size of the finite element model obtained is often irreconcilable with the number of calculations required to obtain all the desired results.

For a limited set of dynamic stresses, there is generally a low-dimensional subspace that makes it possible to describe the dynamic behavior of the structure under specific stresses.

Projecting the model on a restricted basis is called the Ritz or Rayleigh-Ritz method.

This document includes the following points:

• a presentation of Ritz’s methods, their use in linear mode,

• a detail of possible truncation corrections,

• the nonlinear generalization of Ritz methods,

• two simple illustrative examples.