Trouble running code calculating eigenvalues with symbolic variables. takes hours to calculate and gives large unusable answers

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evan watts 2021-10-20

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https://ww2.mathworks.cn/matlabcentral/answers/1567568-trouble-running-code-calculating-eigenvalues-with-symbolic-variables-takes-hours-to-calculate-and-g

评论： evan watts 2021-10-21

I have a code that correctly ouputs the first 8 natural frequencies of a model 8 story tower from the lab. I am trying to change the code with a symbolic E variable with the syms function. I am hoping I can get an answer for the natural frequency that contains the variable E I can rearrange and solve for E (youngs modulus) if I know the natural frequency from lab testing. I have succesfully done this with a much simpler 2Dof problem which i will attach for clarity. However when attempting to run the code on the larger problem it gets stuck when calculating the eigenvalues taking hours to compute and also giving such large results that MATLAB lags. I have reached the limits of my matlab knowledge in trying to fix this. I am hoping that someone may be able to help see something I am missing or show me a new function I'm unsure of or even tell me that what I am attempting is impossible. Thank you

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David Goodmanson 2021-10-21

Hi evan,

If eigenvalue E is symbolic, then there is no getting around the fact that for an nxn matrix M, the requirement det(M-E*I) = 0 is equivalent to finding the roots of an nth degree polynomial in E. But except for special cases, there is no algebraic expression for the roots of an nth degree polynomial for n>=5. So yes, basically impossible. Of course a numerical solution is a different story.

evan watts 2021-10-21