.. _R5.01.02:

**r5.01.02** Solving the modal problem
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**r5.01.02** quadratic (QEP)
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**Summary**

The study of the dynamic stability of a damped and/or rotating structure leads to the resolution of a modal problem that is higher than the traditional standard (SEP) or generalized (GEP) modal problems.

To understand them, **Code_Aster proposes a myriad of methods** **via the operators** **CALC_MODES**: inverse powers and the Müller, Lanczos, IRA and QZ method. They each have their scope of use, their advantages/disadvantages and their development history.

In the first part of the document we summarize the problem of solving a quadratic problem and its variation in the general architecture of a *Code_Aster* modal calculation. Then we detail the numerical, computer and functional aspects of each of the approaches available in the code. The various results, algorithms, or parameters discussed in this document are often based on lower-order modal methods (SEP and GEP) described in document [:ref:`R5.01.01 <R5.01.01>`]. Reading the latter is therefore a recommended prerequisite.




.. toctree::
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    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Introduction
    Contexte
    M_thode_des_puissances_inverses__OPTION_parmi___PROCHE___AJUSTE___
    M_thode_de_sous-espace__METHODE__TRI_DIAG___SORENSEN__
    M_thode_globale_QZ__METHODE__QZ__
    Bibliographie
    Description_des_versions_du_document

    Annexe_1__Interpr_tation_des_valeurs_propres_complexes