Matlab (calculate natural frequencies using eig function)

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SUMMARY

The discussion focuses on calculating natural frequencies using the eig function in MATLAB with specific mass (M), damping (C), and stiffness (K) matrices. The user encountered issues with the matrix A, particularly with the term -M/C resulting in NaN values, which hindered the eig function's execution. The correct formulation of matrix A is crucial for obtaining valid results, and the user needs to ensure that the matrices are properly defined to avoid singularities.

PREREQUISITES
  • Understanding of MATLAB programming and syntax
  • Knowledge of linear algebra, specifically eigenvalues and eigenvectors
  • Familiarity with mechanical system dynamics, including mass, damping, and stiffness matrices
  • Experience with matrix operations in MATLAB, particularly matrix inversion and multiplication
NEXT STEPS
  • Review MATLAB documentation on the eig function for eigenvalue problems
  • Learn about matrix conditioning and how to avoid singular matrices in MATLAB
  • Explore the formulation of state-space representations in dynamic systems
  • Investigate alternative methods for calculating natural frequencies, such as using the 'ss' function in MATLAB
USEFUL FOR

Students and engineers in mechanical and structural dynamics, MATLAB users seeking to solve eigenvalue problems, and anyone interested in analyzing dynamic systems using numerical methods.

Junichirol
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Homework Statement


Determine the corresponding natural frequencies
M = [1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1];
C = [2 0 0 0;0 0 0 0;0 0 0 0; 0 0 0 0];
K = [10 -5 0 0;-5 10 -5 0;0 -5 10 -5;0 0 -5 10];

Homework Equations


A = [zeros (4) eye(4); -M/K -M/C]
[V,D] = eig(A)

The Attempt at a Solution


just need help on A = [zeros (4) eye(4); -M/K -M/C].
-M/C =
NaN NaN NaN NaN
NaN NaN NaN NaN
NaN NaN NaN NaN
NaN NaN NaN -Inf

I also try with -inv(M*C)
-Inf -Inf -Inf -Inf
-Inf -Inf -Inf -Inf
-Inf -Inf -Inf -Inf
-Inf -Inf -Inf -Inf

This matrix caused the [V,D] = eig(A) cannot work.
Any step that i missed up?
 
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Junichirol said:

Homework Statement


Determine the corresponding natural frequencies
M = [1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1];
C = [2 0 0 0;0 0 0 0;0 0 0 0; 0 0 0 0];
K = [10 -5 0 0;-5 10 -5 0;0 -5 10 -5;0 0 -5 10];
Is that really the complete problem your were given?
 
DrClaude said:
Is that really the complete problem your were given?
For a system with the mass, damping, stiffness matrices given as below:
M = [1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1];
C = [2 0 0 0;0 0 0 0;0 0 0 0; 0 0 0 0];
K = [10 -5 0 0;-5 10 -5 0;0 -5 10 -5;0 0 -5 10];
Determine the corresponding natural frequencies by using Matlab eig function.
 

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