Plane Vibrations of a Simply-supported Double Cross

This test lets you check the plane vibration of a simply-supported double cross in the context of a modal (or frequency) case. You will use a 1D mesh.

This test is used to validate the following attributes:

Bending-extension coupling
multiple and close eigen values.

Reference:

NAFEMS-Glasgow, BENCHMARK newsletter, p.14, April 1989.

Specifications

Geometry Specifications

The recommended Finite Element Model uses four beam elements per arm.

Length: `L = 5000 mm`
Height: `h = 125 mm`

Analysis Specifications

Young Modulus (material): `E = 200 GPa`
Poisson's Ratio (material): `ν = 0.3`
Density: `ρ = 8000 Kg/m³`
Restraints: The structure is planar (all out-of plane motion is blocked). The eight ends of the double cross are simply-supported, hence the boundary conditions are: `u = v = 0` at `A`, `B`, ... `H`.

Results

The table below presents the results of the 16 lowest natural frequencies of this structure:

Mode	Reference value [`Hz`]	Computed result [`Hz`]	Error [`%`]
1	11.336	11.336	0
2-3	17.687	17.687	0
4-8	17.715	17.715	0
9	45.477	45.477	0
10-11	57.364	57.364	0
12-16	57.683	57.683	0

To Perform the Test:

The DoubleCross.CATAnalysis document presents a complete analysis of this case.
Proceed as follow:

Open the CATAnalysis document.
Compute the case and generate an image called Deformed mesh.