Modal Analysis:

Modal analysis is a tool that allows to compare measurements and calculation in the low frequency region.

The modes are mainly calulated using the finite element method (FEM).

The measurement is recorded with an artifical excitation either by a shaker or an instrumented hammer. The admittances of the structure are derived using the power spectral density (PSD) of the excitation and the cross power spectral density of the response and the excitation.

The admittances of a discrete model as it is given in the FEM can be described by a quotient of two polynomials. The polynomial in the denominator is the same for all admittances of a structure.  The zeros of the polynomial in the denominator are the complex resonances of the structure.

A large number of methods exist for the esimation of the complex modes from the admittances. In the institute the Global Rational Fractional Polynomial (GRFP) method was implemented. An extension of the method allows to derivate directly the mode shape.