A sloppy explanation is that the solver at some point will work with the ‘dynamic stiffness Ill-conditioned if you set Search for eigenvalues around to be zero. However, they may not match since the complex amplitudes are normalized.įor normalization of eigenvectors, I tried to compare the amplitudes of simple acoustic theoretical real modes (such as cos(Ax)*cos(By)*cos(Cz)) since they are always 1 at the corners. I used LiveLink and eigs function it may be solving with real symmetric solver.įor normalization of eigenvectors, I tried to compare the amplitudes of simple acoustic theoretical real modes (such as cos(Ax) cos(By)cos(Cz)) since they are always 1 at the corners. I could get real eigenvectors and eigenfrequency if I solved these matrices calculated by COMSOL with MATLAB. Is it difficult to obtain perfect real eigenvectors if an nonsymmetric eigenvalue solver is selected? ![]() Study1 and Stud圓 for Acoustic Case and Study2 for Solid Case are examples. Is it correct that each eigenmode possibly have a complex eigenfrequency if I set Search for eigenvalues around to be zero numerically?Īnd about eigenvectors I am most interested in, is it possible for a real symmetric matrix to have complex value regardless the settings about Search for eigenvalues? That's why I have tried Search for eigenvalues around zero.īut in general case, I could understand Search for eigenvalues around frequency should not be zero. In the simple rectangular acoustic with sound hard wall case, I think that the rigid body mode its eigenfrequency is nearly 0Hz is physically important for the comparison with the theoretical solution and the direct solution at low frequency response. Thanks you very much for your very valuable advice. ![]() Then the imaginary contamination will be negligible. The best is if it is close the first non-trivial eigenfrequency. With insufficient boundary conditions, K in itself is singular, and with omega = 0 there is no contribution from the mass matrix.įor such rank deficient problems, you should always use a *Search for eigenvalues around* frequency that is non-zero. A sloppy explanation is that the solver at some point will work with the ‘dynamic stiffness matrix’ -omega^2\*M K, where omega is the given frequency, M is the mass matrix, and K is the stiffness matrix. Such problems are ill-conditioned if you set *Search for eigenvalues around* to be zero. You can trigger the same behavior in Solid Mechanics by disabling the *Fixed Constraint*. The acoustics model shows large imaginary parts in one case: where the shift frequency is zero. ![]() With insufficient boundary conditions, K in itself is singular, and with omega = 0 there is no contribution from the mass matrix.įor such rank deficient problems, you should always use a Search for eigenvalues around frequency that is non-zero. A sloppy explanation is that the solver at some point will work with the ‘dynamic stiffness matrix’ -omega^2*M K, where omega is the given frequency, M is the mass matrix, and K is the stiffness matrix. Such problems are ill-conditioned if you set Search for eigenvalues around to be zero. For structural mechanics, a rocket in space would be without constraints. In particular for acoustics, having sound hard walls everywhere is reasonable. Such boundary conditions are not necessarily physically wrong. For solid mechanics, that means rigid body motions and for acoustics, a constant arbitrary pressure. What happens is that when there are too few Dirichlet conditions, you get eigenvalues that are almost zero (theoretically zero). You can trigger the same behavior in Solid Mechanics by disabling the Fixed Constraint. ![]() I actually want to solve the acoustic problem with damping, but I would like to understand a better settings for these problems because I may be terribly misunderstanding about basic problems. In the solid case, please check on the imaginary part of the results computed by the nonsymmetric solver. In the acoustic case, the eigenvector normalized by the maximum value should be ☑ real value at the corner location. In most case, the imaginary part is always much smaller than the real part. It was created on Japanese language environment but using English label in Studies and Results. When using the nonsymmetric eigenvalue solver, is complex eigenvector always calculated regardless of the characterization of matrices and real eigenvalues (eigenfrequencies)? At first, I'm sorry for that I did not notice that the text "When using a search for eigenfrequencies, the nonsymmetric eigenvalue solver is always used, even when the problem to solve is symmetric" is written in the Reference Manual.
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