pyHarm.Analysis.Linear_Analysis
===============================

.. py:module:: pyHarm.Analysis.Linear_Analysis


Classes
-------

.. autoapisummary::

   pyHarm.Analysis.Linear_Analysis.Linear_Analysis


Module Contents
---------------

.. py:class:: Linear_Analysis(inputData: dict, System: pyHarm.Systems.ABCSystem.ABCSystem)

   Bases: :py:obj:`pyHarm.Analysis.ABCAnalysis.ABCAnalysis`


   Modal analysis and linear forced response analysis.

   Performs a linear modal analysis and then proceeds to a linear FRF by using mode superposition

   .. attribute:: system

      ABCSystem associated with the analysis.

      :type: ABCSystem

   .. attribute:: analysis_options

      input dictionary completed with the default values if keywords are missing.

      :type: dict

   .. attribute:: flag_print

      if True, prints a message after each Solve method.

      :type: bool

   .. attribute:: SolList

      list of SystemSolution stored.

      :type: list[SystemSolution]

   .. attribute:: eigensol

      output dictionary containing the eigenfrequencies and the eigenvectors

      :type: dict


   .. py:attribute:: factory_keyword
      :type:  str
      :value: 'linear_analysis'


      keyword that is used to call the creation of this class in the system factory.

      :type: str


   .. py:attribute:: name
      :value: 'Linear modal and FRF analysis'



   .. py:attribute:: default

      default dictionary for the analysis.

      :type: dict


   .. py:attribute:: system


   .. py:attribute:: analysis_options


   .. py:attribute:: flag_print


   .. py:attribute:: SolList
      :value: []



   .. py:attribute:: eigensol


   .. py:method:: initialise()

      Retrieves the mass and stiffness matrix of the assembled system

      :returns: full stiffness matrix of the system
                M_global (np.ndarray): full mass matrix of the system
      :rtype: K_global (np.ndarray)



   .. py:method:: modal_analysis(K, M)

      Eigenvalue analysis leading to the eigenfrequencies and the normalized right eigenvectors

      :param K: full stiffness matrix of the system
      :type K: np.ndarray
      :param M: full mass matrix of the system
      :type M: np.ndarray

      :returns: eigenfrequencies in rad/s
                phi (np.ndarray): normalized to unity right eigenvectors
      :rtype: omega (np.ndarray)



   .. py:method:: compute_linear_FRF(K, M, phi)

      Linear frequency response function by means of mode superposition

      :param K: full stiffness matrix of the system
      :type K: np.ndarray
      :param M: full mass matrix of the system
      :type M: np.ndarray
      :param phi: normalized to unity right eigenvectors
      :type phi: np.ndarray



   .. py:method:: Solve(x0=None, **kwargs)

      Solving step of the analysis.



   .. py:method:: makeStep(K, M)

      Makes a whole step of the analysis.

      :param K: full stiffness matrix of the system
      :type K: np.ndarray
      :param M: full mass matrix of the system
      :type M: np.ndarray

      :returns: eigenfrequencies in rad/s
                phi (np.ndarray): normalized to unity right eigenvectors
      :rtype: omega (np.ndarray)