# Harmonic Analysis

Harmonic analysis of structures is to calculate the maximum elastic response of a structure subjected to harmonic loading at steady state. The structure responses include nodal displacements, velocities and accelerations as well as element forces and moments etc. The harmonic loading is the load that varies sinusoidally along with time. Harmonic analysis is based on modal dynamic analysis results (frequencies, mode shapes and modal masses etc). It calculates the maximum structure responses for the given harmonic loads using modal superposition method.

This analysis utilizes modal dynamic analysis results, so modal dynamic analysis must be conducted before doing this analysis.

## Modelling implications

Harmonic analysis utilizes modal dynamic analysis results and the construction of GSA model for harmonic analysis is the same as that for modal dynamic analysis. See Modelling implications of Modal dynamic analysis for the requirements of building up a model for harmonic analysis.

The magnitudes and locations of harmonic loads can be defined in the same way of defining a static load. Load combination (e.g. 1.4L1 + 1.6L2) can also be used in harmonic analysis. Harmonic loads vary sinusoidally and its frequency is defined in the ‘Harmonic Analysis’ page of the analysis wizard.

The results of modal dynamic analysis are essential for harmonic analysis, before doing harmonic analysis, at least one modal dynamic analysis task with analysis results must exist.

## Results

The results of a harmonic analysis are the same as that from Response Spectrum Analysis, they include nodal displacements, velocities and accelerations and element forces, moments and stresses etc. The results are not a set of results in equilibrium but the maximum values that can be expected in the whole history of the vibration response. This means that it is not possible to calculate meaningful intermediate forces and moments along individual elements. Any analysis cases or combination cases that include harmonic analysis results will only use linear interpolation of results along the element.

The results can be viewed in the same way as those from other analyses. See section Results Display Options section for viewing the results.

In addition to the normal node and element results mentioned above, chart views that show the nodal responses (e.g. displacement, velocity and acceleration etc) versus harmonic load frequencies are also available.

## See also:

Analysis Wizard : Harmonic Analysis