17.1.2. Calculation of the positions for the vibration shape animation

The vibration shape animation position of the arbitrary node p, the animation frame index i is calculated with the following equation.

\(\mathbf{r}_{p,i}=\mathbf{r}_{p,j}+\mathbf{A}_{r,j}\mathbf{d}_{p,i}'\)

\(\mathbf{d}_{p,i}'=\left[ \begin{matrix} x_{p,i} & y_{p,i} & z_{p,i} \end{matrix} \right]\)

\(x_{p,i}=m_{p,x,f1}sin \left( \frac{2\pi i}{n-1}+ \frac{\alpha _{p,x,f1} \pi}{180} \right)\)

\(y_{p,i}=m_{p,y,f1}sin \left( \frac{2\pi i}{n-1}+ \frac{\alpha _{p,y,f1} \pi}{180} \right)\)

\(z_{p,i}=m_{p,z,f1}sin \left( \frac{2\pi i}{n-1}+ \frac{\alpha _{p,z,f1} \pi}{180} \right)\)

Where,

\(i\) is an index (1,2, … , n) of the animation frame for the vibration shape.

\(n\) is the number of animation frame for the Vibration Shape animation.

\(j\) is always set to the initial configuration (\(\mathbf{r}_{p,j}\) and \(\mathbf{A}_{r,j}\)).

\(\mathbf{r}_{p,j}\) is the initial position of the arbitrary node p.

\(\mathbf{A}_{r,j}\) is the initial orientation matrix of the three reference nodes.

\(f1\) is the selected frequency.

\(m_{p,xyz,f1}\) is the magnitude result of the FFT for the node p.

\(\alpha _{p,xyz,f1}\) is the phase-angle result of the FFT for the node p.