Matlab (calculate natural frequencies using eig function)

In summary, the problem is to determine the natural frequencies of a system with given mass, damping, and stiffness matrices using the eig function in Matlab.
  • #1
Junichirol
3
1

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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  • #2
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?
 
  • #3
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.
 

Related to Matlab (calculate natural frequencies using eig function)

1. How do I calculate natural frequencies using the eig function in Matlab?

The eig function in Matlab can be used to calculate the eigenvalues and eigenvectors of a given matrix. To calculate natural frequencies, you would first need to create a matrix representing the system's dynamic equations. Then, use the eig function on this matrix to obtain the eigenvalues. The square root of these eigenvalues represents the natural frequencies of the system.

2. What is the significance of calculating natural frequencies in a system?

Natural frequencies are important in understanding the dynamic behavior of a system. They represent the frequencies at which a system will naturally vibrate without any external forces or disturbances. This information is useful in designing and analyzing mechanical, electrical, and other systems.

3. Can the eig function be used to calculate natural frequencies for any type of system?

Yes, the eig function can be used to calculate natural frequencies for any type of linear system. However, it is important to note that the eig function assumes that the system is continuous and has no damping. If the system has damping, other techniques may be needed to accurately calculate its natural frequencies.

4. How does the size of the matrix affect the accuracy of the calculated natural frequencies?

The size of the matrix does not affect the accuracy of the calculated natural frequencies. However, the size of the matrix does affect the computational time and memory usage of the eig function. It is recommended to use larger matrices for more accurate results, but this may not always be feasible due to computational limitations.

5. Are there any limitations to using the eig function for calculating natural frequencies?

Yes, there are some limitations to using the eig function for calculating natural frequencies. As mentioned before, the eig function assumes a linear, continuous, and undamped system. It may also produce inaccurate results for systems with repeated eigenvalues. In such cases, it is recommended to use other techniques such as the QR algorithm or the Jacobi method for more accurate results.

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