Modal space - In our own little world

Pete Avitabile discusses the eigensolution and what researchers are attempting to do when they find the frequencies and mode shapes. The first thing that he suggests is that the eigenvalues can be found from the determinant of the matrix. The determinant will really be nothing more than a high order polynomial whose roots are the eigenvalues. These can be obtained numerically from any root solving algorithm such as Secant Method or Newton-Rapson Method. It is important to realize that the eigen solution is used to obtain the eigen-pair, which is frequency and the vector associated with the eigen-equation. Another thing to realize is that the mode shapes are linearly independent and the mode shapes are also orthogonal with respect to the mass and stiffness matrices. This is a by-product of the eigen solution and an important fact, which is used when checking the finite element model with measured experimental data.