Free Vibration of 2D-Structures
Free vibrations of plane beams and frame structures are examined.
Natural frequencies and eigenforms are calculated. The vibrations of the structures in the mode shapes are simulated.
To the model data
A model to be examined is determined by:
- All points where the structure is supported, where local masses are located or where there are cross-sectional jumps.
When entering the point coordinates, you can access the coordinates of other points via x1, y1, x2, y2 etc.
The mouse can be used: double click to create new nodes, click drag to move existing nodes.
- A list of the elements of the structure. For each element its 2 endpoints must be given.
Furthermore, its material index is required (e.g. 1 if only one material is used).
The last entry (type) determines whether it is a beam (type 0), a truss (type 3) or a beam with a hinge at the front (type 1) or at the back (type 2).
You can also create elements with the mouse by clicking and dragging.
- Information on the material. These are cross-sectional area A, area moment of inertia I, modulus of elasticity and material density ρ.
- Information on local masses - if there are any.
If only the parameter m is specified, it is point masses (2 degrees of freedom).
If the parameter J is also specified, this mass moment of inertia is taken into account (3 degrees of freedom).
- Support information. Here you can tie up point-related in both the x and y directions as well as against rotational movement.
Structures can be modeled here with beam elements with and without mass inertia, depending on whether a density ρ is given or not.
In the latter case, the system must have at least one local mass.
If the mass inertia is not given for the beam elements, a fine subdivision of the structure with elements is not necessary.
This is different in the case of beam elements with mass inertia. In this case the more elements are used the more natural frequencies will be calculated.
However, only the smaller of the calculated natural frequencies provide reasonably good approximations.
The finer a model is subdivided by elements, the better the approximations become.
Because the program does not know any units, the user is responsible
to enter consistent input data. It is therefore easiest to use data in the SI unit system.
I.e. Coordinates in m, forces in N, masses in kg, mass moments of inertia in kgm², etc.
Originally, the program should only know about beam elements.
As a small (not entirely successful) extension you can also use springs.
They are the "type 4". Spring stiffness and optional mass are provided via the material properties Ei and ρi.
In principle, springs have the same stiffness matrix as truss elements, only that their stiffness is given directly and is not calculated from AE/L.
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