For structures under dynamic loads, simulations and experiments are frequently used side by side. This leads to mutual benefits. On the one hand, simulation provides a means to identify preferred points to measure. On the other hand, experimental results can be used to identify differences between experimental and simulation model, which provide a basis for model updating to fit the test results by simulation.

One important comparison between experimental modal analysis (EMA) and dynamic eigenvalue analysis is between measured and computed natural frequencies and between measured and computed mode shapes. While the natural frequencies can be compared directly, the comparison of mode shapes is usually made using MAC matrices (MAC - Modal Assurance criterion). To this end, each mode shape of the experiment is compared with each computed mode shape and vice versa. The values of a MAC matrix is between Zero and One. Values near One indicate a strong similarity of the mode shapes, while small values indicate different mode shapes.

PERMAS is capable to read model and results (from a Universal File) and to use them subsequently to generate and export directly the MAC matrix with the computed mode shapes.

The attached figure shows an example, which kindly has been made available by Prof. Dr.-Ing. Jörg Bienert of Ingolstadt University of Applied Sciences. He has determined the experimental results for the ladder frame structure, while the simulation and the comparison have been made by INTES. The location of the sensors does not fit to nodes of the FE mesh. So, interpolation regions were used to connect the sensor locations with the neighboured nodes of the FE mesh. By doing so, the computed results are available at the same points as the measured results and the comparison can be performed directly by generating the corresponding MAC matrix.

For the first three modes, the computed and measured natural frequencies and mode shapes are shown. We see from the MAC matrix that the modes four to seven were not available in the experimental results. The experiment used one-dimensional sensors, which perfectly detect displacements normal to the ladder frame. But the computed modes four to seven show displacements in the plane of the ladder frame, which are not detectable by the used sensors.

Comparison of dynamic results from experiment and analysis