# Harmonic¶

The analysis type **Harmonic** enables you to simulate the steady state
structural response of solids subject to periodical (sinusoidal) loads.
Similar to a transient dynamic analysis inertia effects are taken into account,
but in contrast to a transient analysis the results are not time-dependent, but
frequency-dependent, making it possible to compute the response of a structure
subjected to vibrating forces or displacements over a whole frequency
spectrum.

As this is a linear simulation type only linear elastic materials are supported, but damping effects can be taken into account.

All of the linear boundary conditions are available for this simulation type and the loadings can depend on the excitation frequency.

In contrast to the other simulation types the results of the **Harmonic** analysis are
of complex nature and the user specifies in the *Result Control* section how the
complex results are exported. Possible choices are either *magnitude and phase* pair
or *real and imaginary* part.

Specifically useful for a **Harmonic** analysis are probe points, which also can be
assigned in the *Result Control* section under *Point data*. They are used to monitor
the response of the system at specific sensor points, enabling the comparison of
simulation results with measured data.

A *Frequency* analysis is always a good starting
point before performing a **Harmonic** analysis.

## Domain¶

For a **Harmonic** analysis either a first or second order mesh can be used.
If the structural response should be monitored at a specific point, the user can define them with
the *Geometry Primitives* functionality. By creating a new
Geometry Primitive Point at specified coordinates this point can later be used in the
*Result Control* section in a Point Data item.

## Model¶

After having either produced a mesh from your geometry on the SimScale platform or uploaded it directly, you may declare the basic properties of the model.

### Materials¶

You can define the material properties of one or multiple solids in the materials section. Depending on the material law that you choose, you have to specify different properties.

For **Harmonic** only linear elastic material can be defined. As
it is a dynamic analysis type in addition to the *Young’s modulus*
and the *Poisson’s ratio*, the *density* of the material is required. Please see the *Materials* section for more details.

There are two *material damping* models available for a **Harmonic** analysis:

### Boundary conditions¶

For a **Harmonic** analysis the user doesn’t need to worry about the sinusoidal application
of the boundary conditions as this is done implicitly. In addition to the
standard input parameters for each boundary condition the user can specifically
define a phase angle for each boundary condition which allows to take into
account phase offsets between different boundary conditions.
For most of the boundary conditions the specified values can depend on the
excitation frequency and can thus be variable over the frequency range.
For vector-valued boundary conditions this can be achieved via the scaling parameter
which can be defined as a scalar, a function of frequency or as table data. For
scalar-valued boundary conditions this directly applies to the scalar value.

Available Constraint types (Displacement boundary conditions):

Available Load types (Force boundary conditions):

## Numerics¶

Under numerics you can set the equation solver for your simulation.
For a **Harmonic** analysis there are three direct *linear solvers* available:

## Simulation control¶

Under *simulation control* you are able to set frequency range for your simulation.
You can either choose a single frequency or a frequency list. The frequency list
is defined via the start and the end frequency and a frequency stepping length.

In the Simulation control also the desired *number of computing cores* is selected as
well as the *maximum allowed runtime* of the simulation run.

## Result Control¶

In the result control section the data fields that should be calculated as well as additional derived data can be specified.

### Solution Fields¶

The fields that should be calculated and stored in the result data have to be defined
via the Solution Fields. For a **Harmonic** analysis besides the field type also the complex
numbers representations have to be defined for each solution field.

### Point Data¶

Here the Point Data items can be defined in order to monitor the structural response
at specific spatial points. The point where the desired data should be evaluated have
to be defined via geometry primitives. This geometry primitives can either be defined
directly by using the “*Create new geometry primitive*” button or predefined geometry
primitive points of the Domain section can be referred to.

Usually this points are used to compare the numerical results to measured data at a corresponding sensor point or to directly extract data at a critical point of the structure.

### Solver¶

Currently harmonic analyses are solved on the SimScale platform
using the finite element code Code_Aster. See our
*Third-party software section* for further
information.