OS-V: 0435 Clamped Thick Rhombic Plate

Test No. FV22 The behavior of distorted, thick elements in normal modes analysis is examined using OptiStruct.

Model Files

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

fv22.fem

Benchmark Model

The 4-node quad elements with 10x10 mesh configuration are used to model the thick rhombic plate. The x-translation, y-translation displacements, and z-rotational displacements are fixed for all of the nodes. In addition, the z-translation, x-rotational and y-rotational are fixed for the nodes along the four edges.

The material properties are:

Property: Value
E: 200 x 10⁹ N/m²
$υ$: 0.3
$ρ$: 8000 kg/m³

Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution. The closed form solution is not available for mode 6, the target value for H.O.E. should be used instead.

f*: Closed form solution

Mode 1		Mode 2		Mode 3

`f*` CQUAD4	133.95 Hz 0.9937	`f*` CQUAD4	201.41 Hz 1.0382	`f*` CQUAD4	265.81 Hz 1.0633

Mode 4		Mode 5		Mode 6

`f*` CQUAD4	283.68 Hz 1.0006	`f*` CQUAD4	334.45 Hz 1.1073	F[HOE] CQUAD4	386.62 Hz 1.0403

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis