Introduction to computational Mechanics, TMHL63, vt 1, 2014

modified 2014-02-07

Laboratory problem IV

Eigenvibration analysis by FEM

You arehere to use the commercial FE-code ANSYS for analyzing the eigenvibration of a simply supported beam. More specifically, you are to consider a simply supported slender beam, as illustrated below, for which you should find eigenfrequencies and associated eigenmodes.

Details

For the geometry and loading you are to use the values L=1m, h=20mm and b=20mm. The factor α is
1.01for group 1
1.022
…
1.1111
etc

An isotropic and linear elastic steel material can be assumed (the default material in ANSYS).

You are to perform a 2D-analysis. Please observe, that the first thing you are to do (i.e. even before opening the geometry modeler) is to set the analysis type to 2D; thus ensuring to get plane elements.

You are to start with 20 elements along the beam and one element in the height direction (default element type), and compare the result with the analytical one. Then you are to refine the mesh to 40 elements along the beam and two elements in the height direction, which will give you a somewhat better result. The element mesh to be used can be obtained by so called “edge sizing” operations.

The eigenfrequency formula for a simply supported beam can be found at the end of the notes to Lecture 14, where also some mode shapes can be found.

Reporting

The evaluation/reporting of this lab work is to be carried out by reporting to the teacher by using the reporting form found on the next page. More precisely this, and exactly this (no more and no less) is to be handed in both electronically and in printed form (in colour)

  • The two lowest eigenfrequencies found analytically and by FEM- they should be rather close. (on the reporting form).
  • A plot from ANSYS showing the second eigenmode with the finer/denser mesh (40 x 2 elements) visible(electronically and attached to the reporting form)

Please Observe! Do NOT send this report together with the report for Lab Ior Lab II, and do NOT send in zipped archives!

Note:

The reporting (in electronic and printed form, the latter in the bookshelf in the corridor of Solid Mechanics) is to be done no later than 18:00, Friday, March 14:th

GOOD LUCK!

Reporting

Lab IV, TMHL63, vt 1, 2014

(fill in the form electronically!)

Group ….

Namepersonal numbere-mail

1

2

3

First/lowest eigenfrequency found analytically......

First/lowest eigenfrequency found by FEM
(for fine/dense mesh)......

Second eigenfrequency found analytically......

Second eigenfrequency found by FEM
(for fine/dense mesh)......

The ANSYS plot for the second eigenmodeis to be attached to this form (for the printed reporting).