The flexible beam is created using the Modelica.Mechanics.MultiBody library components. Flexible beam is approximated by the rigid bodies and joints coupled with springs and dampers. Flexible beam is discretized into N+1 body boxes and N revolute joints which provides the flexibility features to the model. And, N spring-damper components are placed to the revolute joints. The spring stiffness coefficients are determined depending on the material properties and the geometry of the flexible beam while damping coefficients are taken very small. Modeling was adopted from the paper "Modeling Flexible Bodies in SimMechanics" by Victor Chudnovsky, Arnav Mukherjee, Jeff Wendlandt and Dallas Kennedy which was intended for MATLAB and Simulink environment.
The flexible beam is discretized into elements, and a single element is considered to be consisted of 2 body boxes and a revolute joint between these body boxes. If we assign length l to a single element, each body box in this element will have the length of l/2. By connecting each element together a flexible beam is obtained. Each element along the length of the beam is taken to be identical, therefore, the flexibility of the beam is uniform along its length. A single element of the flexible beam is as in the figure below.
A flexible beam containing 2 elements is as shown in the figure below:
A force is applied for a period of time at the tip of the flexible beam in order to create vibration. Parameters for the FlexibleBeamModelica:
| Parameters | Comment |
|---|---|
| N | number of elements |
| L | length of the flexible beam |
| l | length of each bodybox |
| W | width of the beam |
| H | heigth of the beam |
| D | density of the material |
| E | young's modulus of the material |
| J | area moment of inertia |
| DampCoeff | rotational damping constant |
| SpringCoeff | rotational spring constant |
| F | force component at y-axis |