OS-V: 0400 Pin-ended Double Cross

Test No. FV2 A pin-ended double cross, in-plane vibration problem. OptiStruct is used to investigate the coupling between flexural and extensional behavior, as well as the repeated and closed eigenvalues of the double cross in Normal Modes Analysis.

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

fv2.fem

Benchmark Model

The 2-node simple beam elements are used to model the double cross. Each arm of the cross consists of four elements. The x- and y-translation displacements are fixed at the end of all arms.

The material properties are:

Property: Value
E: 200 x 10⁹ N/m²
$ρ$: 8000 kg/m³

Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution.

f*: Closed form solution

Mode 1		Modes 2 and 3		Modes 4, 5, 6, 7 and 8

`f*` CBAR	11.336 Hz 0.9984	`f*` CBAR	17.709 Hz 0.9958	`f*` CBAR	17.709 Hz 0.9974

Mode 9		Modes 10 and 11		Modes 12, 13, 14, 15 and 16

`f*` CBAR	45.345 Hz 1.0000	`f*` CBAR	57.390 Hz .9944	`f*` CBAR	57.390 Hz 0.9999

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis