.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/analyses/cyclic/example_rotor_sector.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_analyses_cyclic_example_rotor_sector.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_analyses_cyclic_example_rotor_sector.py:


Cyclic-symmetry modal on a rotor sector
=======================================

A rotor with :math:`N` identical sectors spanning 360° has a spectrum
that factors by *harmonic index* :math:`k \in \{0, 1, \dots, N/2\}`.
Analysing one base sector plus the constraint

.. math::

    u_\text{high} = e^{i k \alpha}\, R(\alpha)\, u_\text{low},
    \qquad \alpha = 2\pi / N,

recovers the full-rotor spectrum at a fraction of the DOF count.

This example builds a simple 4-sector rotor from a pyvista annular
sector, wraps it in a :class:`~femorph_solver.CyclicModel`, and runs
:meth:`~femorph_solver.CyclicModel.modal_solve` across all harmonic
indices.  ``CyclicModel`` auto-detects the low/high cyclic faces from
the rotation axis and angle, so the caller never has to assemble a
manual DOF pair list.

.. GENERATED FROM PYTHON SOURCE LINES 23-32

.. code-block:: Python


    from __future__ import annotations

    import numpy as np
    import pyvista as pv

    import femorph_solver as fs
    from femorph_solver import ELEMENTS








.. GENERATED FROM PYTHON SOURCE LINES 33-35

Build a 90° annular sector
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 35-51

.. code-block:: Python

    N_SECTORS = 4
    ALPHA = 2.0 * np.pi / N_SECTORS

    N_T, N_R, N_Z = 12, 6, 3
    theta = np.linspace(0.0, ALPHA, N_T + 1)
    r = np.linspace(0.8, 1.0, N_R + 1)
    z = np.linspace(0.0, 0.1, N_Z + 1)

    # (r, θ, z) order gives a CCW-from-above hex winding in the (r, θ)
    # plane — swapping r and θ would flip the winding inside-out.
    R, T, Z = np.meshgrid(r, theta, z, indexing="ij")
    X = R * np.cos(T)
    Y = R * np.sin(T)

    grid = pv.StructuredGrid(X, Y, Z).cast_to_unstructured_grid()








.. GENERATED FROM PYTHON SOURCE LINES 52-59

Wrap as a CyclicModel
---------------------
``CyclicModel.from_grid`` builds the underlying base-sector
:class:`~femorph_solver.Model`, detects the cyclic face pairs from
the rotation axis (default ``"z"``) + ``n_sectors``, and validates
that every low-face point has a rotated counterpart on the high
face within ``pair_tol``.

.. GENERATED FROM PYTHON SOURCE LINES 59-65

.. code-block:: Python

    cm = fs.CyclicModel.from_grid(grid, n_sectors=N_SECTORS)

    # Per-sector physics — element kernel + isotropic material — is set
    # on the inner Model exactly as for a non-cyclic analysis.
    cm.assign(ELEMENTS.HEX8, material={"EX": 2.1e11, "PRXY": 0.30, "DENS": 7850.0})








.. GENERATED FROM PYTHON SOURCE LINES 66-71

Solve every harmonic index
--------------------------
``modal_solve`` defaults to all harmonics ``k = 0 … N/2``, returning
one :class:`~femorph_solver.solvers.cyclic.CyclicModalResult` per
harmonic.  Each result carries ``frequency`` and ``mode_shapes``.

.. GENERATED FROM PYTHON SOURCE LINES 71-78

.. code-block:: Python

    results = cm.modal_solve(n_modes=4)

    print(f"Cyclic modal on {N_SECTORS}-sector rotor:")
    for res in results:
        fs_str = ", ".join(f"{f:.2f}" for f in res.frequency[:4])
        print(f"  k = {res.harmonic_index}: f [Hz] = [{fs_str}]")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Cyclic modal on 4-sector rotor:
      k = 0: f [Hz] = [0.00, 0.00, 503.32, 503.32]
      k = 1: f [Hz] = [0.00, 0.00, 262.09, 452.92]
      k = 2: f [Hz] = [91.75, 91.75, 164.68, 164.68]




.. GENERATED FROM PYTHON SOURCE LINES 79-81

Visualise mode 0 of k = 1
-------------------------

.. GENERATED FROM PYTHON SOURCE LINES 81-94

.. code-block:: Python

    r1 = next(res for res in results if res.harmonic_index == 1)
    phi = r1.mode_shapes[:, 0].reshape(-1, 3)
    grid.point_data["mode_k1"] = np.abs(phi)

    plotter = pv.Plotter(off_screen=True)
    plotter.add_mesh(
        grid.warp_by_vector("mode_k1", factor=0.05 / (np.max(np.abs(phi)) + 1e-30)),
        scalars=np.linalg.norm(phi, axis=1),
        cmap="viridis",
        scalar_bar_args={"title": f"|mode| (k=1, f={r1.frequency[0]:.1f} Hz)"},
    )
    plotter.add_axes()
    plotter.show()



.. image-sg:: /gallery/analyses/cyclic/images/sphx_glr_example_rotor_sector_001.png
   :alt: example rotor sector
   :srcset: /gallery/analyses/cyclic/images/sphx_glr_example_rotor_sector_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.209 seconds)


.. _sphx_glr_download_gallery_analyses_cyclic_example_rotor_sector.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: example_rotor_sector.ipynb <example_rotor_sector.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: example_rotor_sector.py <example_rotor_sector.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: example_rotor_sector.zip <example_rotor_sector.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_