Rod

Massless flexible rod

 Description The Rod component models a massless flexible rod. Rod can be seen as a spring/damper connection between two end frames with a given unstretched length and spring/damping constants.

Connections

 Name Description Modelica ID $\mathrm{frame__a}$ Frame on one end of the rod frame_a $\mathrm{frame__b}$ Frame on the other end of the rod frame_b

Parameters

 Name Default Units Description Modelica ID $\mathrm{L__0}$ $1$ $m$ Unstretched length of the rod L0 $\mathrm{K__s}$ $\frac{N}{m}$ Spring constant Kspring $\mathrm{K__d}$ $\frac{N\cdot s}{m}$ Damping constant Kdamper Show visualization true - True means the disk geometry is visible in the 3-D playback visualization $r$ 0.01 $m$ Rod radius used for visualization only r Color - Rod color in the 3-D playback color Transparent false - True means the geometry is transparent in the 3-D playback transparent

 Equations Assuming that the translation vector, $\mathbf{r}$, is directed from frame_a, to frame_b, $\left[\mathrm{X2},\mathrm{Y2},\mathrm{Z2}\right]$, the resultant forces of the rod are ${\mathbf{f}}_{1}=\frac{f}{‖\mathbf{r}‖}\mathbf{\cdot }\left(\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{X1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{X1}}+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Y1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Y1}}+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Z1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Z1}}\right)$ ${\mathbf{f}}_{2}=-\frac{f}{‖\mathbf{r}‖}\mathbf{\cdot }\left(\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{X2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{X2}}+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Y2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Y2}}+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Z2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Z2}}\right)$ where denotes unit vectors and and are the reaction forces applied to frame_a and frame_b, respectively, and where is the instantaneous rod length. Note that in these equations, bold non-italic symbols denote vectors. Figure 1 shows the rod and the end frames. Figure 1: Rod and end frames