4. Loads

It is assumed that the load was broken down according to the same basis as the movements, i.e.:

\(\mathrm{f}\mathrm{=}\mathrm{\sum }_{l\mathrm{=}0}^{\mathrm{\infty }}\left[(\begin{array}{ccc}\text{cos}l\theta & & 0\\ & \text{cos}l\theta & \\ 0& & \mathrm{-}\text{sin}l\theta \end{array}){\mathrm{F}}_{l}^{s}+(\begin{array}{ccc}\text{sin}l\theta & & 0\\ & \text{sin}l\theta & \\ 0& & \text{cos}l\theta \end{array}){\mathrm{F}}_{l}^{a}\right]\)

There is no coupling for the same harmonic between the parts symmetric and antisymmetric of the load due to the orthogonality of the trigonometric functions \(\text{sin}l\theta\) and \(\text{cos}l\theta\), this for all types of loading. In particular, this means that the equivalent nodal forces are the same for symmetric and antisymmetric harmonics if amplitudes \({F}_{l}^{s}\text{et}{F}_{l}^{a}\) are the same.

For the nature of the loads allowed with Fourier modeling, refer to the user manual [U2.01.07].