2. Objective of the test case, validation#

The objective of the test case is to validate the following commands in particular:

  • MAC_MODES: calculation of the MAC matrix between two modal bases,

  • LIRE_RESU: reading experimental data in IDEAS format,

  • MACRO_EXPANS: expansion of data measured on a numerical model made up of a « judicious » distortion base.

The test case is based on the garteur benchmark (

`www.garteur.eu`_ < http://www.garteur.eu/>, European aeronautical research group).

The test case here is trivial: the experimental data (FRF and eigenmodes) were first calculated numerically before being exported in the IDEAS format. Their expansion on the same numerical model should therefore make it possible to find exactly the expected data.

2.1. Conduct of the test case#

  • Digital model:

    • Definition and calculation of the modal base of the numerical model,

    • Extraction of modes according to their effective mass in the three directions (with EXTR_MODES)

    • Calculation of the correlation matrix between two modal bases with MAC_MODES: this calculation is done to check the orthogonality of the base MODESORT.

  • Experimental model:

    • Definition of the experimental model: the values of the mechanical characteristics are arbitrary, they are only used to create coherent data structures for reading the experimental data,

    • Reading the experimental harmonic response,

    • Expansion of the experimental response on the numerical model (MACRO_EXPANS),

    • Reading the experimental modes,

    • Expansion of experimental modes on the numerical model.

The expansion of the experimental data with MACRO_EXPANS consists in the succession of commands PROJ_MESU_MODAL and REST_GENE_PHYS (and PROJ_CHAMP, for verification). The objective is to find the best combination of the eigenvectors contained in the numerical base in front of the keyword BASE that correctly reproduce the behavior of the experimental data. Provided that the modeling correctly reflects the physics of the measured structure, the experimental data is interpolated with the deformations contained in the numerical model.

  • Modeling A: expansion of the FRF defined on the experimental model on a basis composed of the dynamic modes of the structure, and expansion of the natural modes identified on the experimental model on the same expansion base,

  • B modeling: expansion of the eigenmodes identified on the experimental model using an expansion base composed of static deformations defined on a part of the DDL of the numerical structure.

2.2. Validation of results#

The results are tested by expansion/reprojection. Therefore, no external reference to the calculation needs to be defined. For modeling a, the following tests are carried out:

  • test of the orthogonality of the natural modes extracted MODESY (5 modes): the matrix obtained is the unit matrix,

Component

Reference

Matrix obtained by MAC_MODES

SOMM

\(5.0\)

  • FRF extended: test the differences between experimental FRF and FRF extended/reprojected, on a component of three nodes: the following ratio is calculated:

\(R\mathrm{=}\frac{\mathit{RMS}(∣{\mathit{FRF}}_{\mathrm{exp}}\mathrm{-}{\mathit{FRF}}_{\mathit{et}}∣)}{\mathit{RMS}({\mathit{FRF}}_{\mathrm{exp}})}\)

  • extended proper modes: test the orthogonality of the extended base, by doing MAC of it by itself (MAC_ET),

  • extended eigenmodes: testing the diagonal components of the MAC matrix between extended modes numerical modes (MAC_ETNX), for modeling A, and between extended/reprojected modes and experimental modes for modeling B (MAC_RDEX).