Torsional rotor dynamics - Types of permanent excitation

It's worth remembering that if a real system vibrates permanently, it's because it's excited. In this paragraph, we're interested in permanent excitations whose variation over time is periodic. These excitations are external to the part of the installation being modeled, and must periodically contribute a quantity of mechanical energy which will, at the same time, be transformed into heat by dissipative phenomena. The latter are always present in reality, however weak they may be. If the chosen type of analysis leads to the use of a linear model, it is important to decompose the real excitation into Fourier series. The linear character of the model will enable us, using the principle of superposition, to reconstruct the overall vibration response, from the responses obtained for each harmonic of the excitation.

For a linear model, any excitation can therefore be represented by a sum of elementary sinusoidal or harmonic excitations. Each of these, denoted F _q is defined by its pulsation Ω _q , its amplitude C _q and, its phase Φ _q measured relative to a given time origin.

It can be written as : $F_q=C_q\text{cos}\left({\Omega }_{q}t+{\Phi }_q\right)$

Of these three characteristics, pulsation is by far the most important in practice. It's easy enough to identify, and its value will be defined in each case. Determining the amplitudes and phases of excitations, on the other hand, is generally a complex task which may require modelling specific to each case encountered, and whose results also need to be confirmed by experiment.