2. Benchmark solution#

2.1. Calculation method used for the reference solution#

the reference solution proposed by NAFEMS [bib1] was obtained from a finite element calculation \(\mathrm{3D}\) with brick elements at 20 nodes and with a mesh \(4\times 4\) (plane \(\mathrm{xy}\)) and 1 element depending on the thickness.

2.2. Benchmark results#

The first 7 non-zero frequencies and the associated natural modes, the first three modes are those of rigid bodies:

  • Frequency (mode 4 off plane)

:

\(44.762\mathrm{hz}\)

  • Frequency (modes 5 & 6 off plane)

:

\(110.52\mathrm{hz}\)

  • Frequency (mode 7 out of plane)

:

\(169.08\mathrm{hz}\)

  • Frequency (Mode 8 in the plan)

:

\(193.93\mathrm{hz}\)

  • Frequency (mode 9 & 10 in the plan)

:

\(206.64\mathrm{hz}\)
_images/1000000000000275000000CB04B52C92D4573BCC.png
_images/1000000000000269000000BAD13E83C29D00E004.png

Mode 4 off plane

5&6 mode off plan
_images/1000000000000260000000B7845CDD7072BF6385.png _images/1000000000000281000001C1D746A6F2798DC9AD.png

Mode 7 off plan

Mode 8 in the plan
_images/100000000000020A000001DDBDD065004DECCAA5.png

9&10 mode in the map

2.3. Uncertainties about the solution#

\(\text{< 2\%}\) for a mesh identical to that of [§2.1], i.e. with few elements.

2.4. Bibliographical references#

  1. NAFEMS: The standard NAFEMS Benchmarks, TNSB, Rev. 3, October 5, 1990.