# Coupled Sierra/SM - Sierra/SD Eigenvalue Problems

In this section, a modal analysis is applied to the output of Sierra/SM,
also known as Adagio. A nonlinear preload is computed in Sierra/SM,
followed by a modal analysis in Sierra/SD. In this approach, the modal
analysis is performed about the nonlinear state that is computed in
Sierra/SM. This is the most convenient approach, since the modes about
the deformed state are typically of most interest.

This file transfer approach proceeds as follows. Here the Sierra/SM and
Sierra/SD input decks are named `sierra.i` and `sd.inp`. The model
consists of four layers of material, with a membrane layer between the
bottom layers, as shown in Figure {numref}`%s <fig:sm-transfer>`.

1.  Construct the input decks `sierra.i` and `sd.inp`. Both input decks
    contain modifications required for hand-off as described in Section
    {numref}`%s <section:sm:input>`.

2.  Execute Sierra/SM

3.  The output Exodus file that is assigned in Sierra/SM is used as the
    geometry file for the Sierra/SD analysis. This step will need to be
    inserted manually by the user.

4.  Execute Sierra/SD.

    a)  Read displacements, stresses and certain material parameters
        from previous SM analysis. These are found in the Exodus output
        from SM.

    b)  Update original coordinates to the deformed coordinates,
        $X = X_o + U$.

    c)  Compute element stiffness matrices from material properties.

    d)  Adjust stiffness matrices for stress preload.

    e)  Generate constraints.

    f)  Assemble system level matrices and solve eigenvalue problem.

5.  Eigenvalues and modal frequencies are listed in the `salinas.rslt`
    file. Both modal frequencies and mode shapes are in the file
    Sierra/SD output Exodus file. If as shown here the second case is
    named `two`, then the output Exodus file is named `salinas-two.exo`
    (see example below).

:::{figure-md} fig:sm-transfer

![](sm-transfer.png)

SM/SD Transfer Model Geometry.
:::

:::{only} goodyear
For tire models, the `thickness scale factor` variable in the
Sierra/SM input deck is required for a coupled
Sierra/SM-Sierra/SD analysis. This parameter is the same as the fiber
diameter, which is specified in the material section for the membranes.
This parameter is needed for the coupled analysis, because it is used to
determine the modulus of the fibers, which are in turn used in
Sierra/SD to construct the stiffness matrix.
:::
