(Code_Aster Solver)

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.

Harmonic analysis of two different designs of holder

Harmonic analysis of two different designs of holder

Response plot of two different designs of holder

Response plot of two different designs of holder


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.


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.


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):


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.


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.