Roots switching in an eigenvalue eigenvector problem as a function of frequency

Question

Jeff 2013-11-29

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https://ww2.mathworks.cn/matlabcentral/answers/108018-roots-switching-in-an-eigenvalue-eigenvector-problem-as-a-function-of-frequency

评论： Jeff 2013-11-29

Hello,

I'm solving a system of 4 equations and 4 unknowns as a function of frequency and wavenumber. I'd like to find the dispersion relation of the system.

To do this I'm using the Matlab symbolic math toolbox and solving the following.

k_symbolic=solve(det(M)==0,k); %det(M) is of the form Ak^4 + Bk^2 + C

where M is my matrix representing my system of equations and k is the wavenumber.

I then substitute values for frequency as follows.

k_numeric=subs(k_symbolic,{omega},{2*pi*(1:1000)}) % or whatever frequency range I want

My problem is that when I plot my roots as a function of frequency (k_numeric(omega)) it is clear that the roots are switching. In other words the first root will continue as expected then there will be a discontinuous jump (at say 5 Hz) to the other root solution and vice-versa.

I'd like k_numeric(x) to always be the same root independent of frequency. Is this possible?

Thanks for your help!

Jeff

More details: I'm actually using subs to replace other symbolic values with numeric values which include bessel functions (not sure if this influences anything).