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I am trying to write a MATLAb code for determining the natural frequencies of a first-order shear deformation plate using Ritz method. I am using Legendre polynomials as trial functions in Ritz method, and my code works well for static analysis of plate. I have solved few structural problems with my code and compared the results with MSC NASTRAN. The results are accurate with maximum error of 5%.

However, when I try to find eigenvalues, at least one eigenvalue comes out to be negative. Also, the eigenvalues do not match with eigenvalues obtained from MSC NASTRAN (Modal Analysis).

Is it possible for a plate to have negative eigenvalues?

Ali Baig
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  • May I ask if you can provide the Matlab code for the Ritz method based on FSDT theory？ My email is 412146266@sjtu.edu.cn – user48381 Jun 15 '24 at 11:35

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The only way you can get negative eigenvalues is by including stress stiffness effects (sometimes called "geometric stiffness"), if there are compressive stresses which would cause the plate to buckle.

There can be zero eigenvalues if the plate can move as a rigid body, of course, and they might be calculated as small negative numbers, but those should be a few orders of magnitude smaller that the first positive eigenvalue.

FWIW "accurate to within 5%" probably means "wrong". Try to find a load case where the exact solution is known.

Plotting the deformed shape for your negative eigenvalues might help to find the error - or at least convince you they really are wrong, if the shapes look crazy.

alephzero
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