# Summary

Harmonic Analysis is a common dynamic analysis. In this course, we discussed how to perform the analysis as well as how to interpret the results. Let’s summarize the key points from each lesson.

Performing Mode Superposition Harmonic Analysis

• Harmonic analysis solves for the steady-state dynamic response to sinusoidally repeating loading.
• Harmonic analysis is linear so nonlinearities are ignored.
• The mode superposition method is an efficient method for solving harmonic analysis.
• The excitation and the response have the same frequency, but there may be a lag between them.
• Damping is present in most mechanical systems, so it should be specified to achieve more accurate results and avoid an unrealistically high response at resonance.

Correctly Interpreting Harmonic Results

• The response is steady-state sinusoidal, and we can calculate the amplitude and phase angle of the response.
• It is typical to check the frequency response plots first to find the frequency and phase angle at the peak response(s).
• The contour plots of interest at the peak response(s) can then be investigated.
• The spatial resolution setting of “average” will not report the maximum response depending on the scoping, so care should be taken to set this appropriately.
• It is often necessary to extract multiple results to gain a complete understanding of the harmonic response of the structure.

Utilizing Residual Vector Method in Harmonic Analysis

• Residual vectors can be utilized to achieve accurate results with fewer modes.
• The effect is most evident in cases where the structure has localized deformations.
• The method can be utilized in structures that are meshed with element types of solid, beam, and shell.

Frequency Based Fatigue using Harmonic Analysis

• There are specific cases where the MSUP method cannot be used, for example systems with moderate or significant damping or systems with unsymmetrical matrices. For such cases, we need to perform Harmonic Analysis using the Full Method.
• For calculating the structure’s response, the MSUP method linearly combines the factored mode shapes from a modal analysis. It is generally recommended for most problems with light damping due to its speed and ability to cluster results.
• The full method solves the full system matrices directly. It is an exact solution as compared to the approximations of the mode-superposition method. However, the full method is more computationally expensive.

Performing Harmonic Analysis with Full Method

• The response is steady-state sinusoidal, and we can calculate the amplitude and phase angle of the response.
• It is typical to check the frequency response plots first to find the frequency and phase angle at the peak response(s).
• The contour plots of interest at the peak response(s) can then be investigated.