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After successful completion of the course, students are able to... derive the free oscillation eigenvalue problem and interpret its results, i.e. model shapes and natural frequencies, as well as be familiar with the most important numerical solution methods derive reduced order models for multi degree of freedom systems by using an appropriate modal basis Conduct harmonic response analyses of full and reduced systems, incorporating different damping methods, and be familiar with the concept of transfer functions Describe the working principles of measurement equipment for experimental modal analysis, and to use such equipment in practice Extract natural frequencies and mode shapes from measurement data by using various identification techniques, as well as compare experimentally determined modes to computational results based on appropriate criteria

Jupyter Notebook 99.96% GLSL 0.01% Shell 0.01% Python 0.04%

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Assign TODO for HW 1

Tasks
Eigenvalue Solvers
1 vector iteration (M,P)
2 inverse vector iteration (M,P)
3 Rayleigh quotient iteration (M,P)
4 higher eigenvalues using inverse vector iteration in orthogonal direction (M,P)
5 QR-algorithm (R)
6 subspace-iteration (M,P)
7 numpy/matlab ((M,P)

Eigenvalues and Mode Shapes
1 Visualize the structure of the system matrices (e.g. as image) (T)
2 Visualize the geometry (see template) (T)
3 Compute a different static problem (R)
4 Compute and visualise natural frequencies and oscillation modes for different boundary (T)conditions: free, east edge (x = xmin) clamped , all edges clamped (T)

Submission for HW1
1 Function for vector iteration (M,P,R,T)
2 Compute and plot mode shapes for rectangular plate (free-free) (M,P,R,T)

Legend:
M...Maxi
P...Phili
R...Richi
T...Tae-Hyongi

Eigenvalues and Mode Shapes

1 Visualize the structure of the system matrices (e.g. as image) (T)
2 Visualize the geometry (see template) (T)
3 Compute a different static problem (R)
4 Compute and visualise natural frequencies and oscillation modes for different boundary (T)conditions: free, east edge (x = xmin) clamped , all edges clamped (T)

Team Name

Jeder überlegt einen Vorschlag bis zum 1. Meeting am 11.03.

Eigenvalue Solvers implementation - except QR

Eigenvalue Solvers
1 vector iteration (M,P)
2 inverse vector iteration (M,P)
3 Rayleigh quotient iteration (M,P)
4 higher eigenvalues using inverse vector iteration in orthogonal direction (M,P)
6 subspace-iteration (M,P)

Submission for HW1

  • Function for vector iteration (M,P,R,T)
  • Compute and plot mode shapes for rectangular plate (free-free) (M,P,R,T)
  • Documentation and upload to TUWEL

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