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CATIA Analysis ­ Tips & Tricks

Ensuring Accurate Results When Performing Harmonic Response Analysis in CATIA V5 Analysis

In a structural system, such as an aircraft, any sustained cyclic load will potentially produce a harmonic response. This could result in accelerating fatigue or other harmful effects of cyclic vibrations. Performing harmonic analysis with finite element analysis (FEA) software enables designers and engineers to determine the steady-state response of a linear structure subjected to loads that vary sinusoidally (harmonically) with time. CATIA V5 Analysis provides the capabilities to calculate the modes and natural frequencies needed to simulate the vibration characteristics of product designs. The GDY (Generative Dynamic Response Analysis) product within the CATIA V5 Analysis suite takes this a step further by letting users study the response of their designs to dynamic loading, allowing them to ensure early in the design phase that their designs do not suffer from resonance and other dynamic effects. GDY provides both transient and harmonic analysis. Transient analysis allows the response of the structure to be determined for loading that varies quite generally with time. Harmonic analysis assumes that the time variation of the loading is sinusoidal, but allows the response of the structure to be predicted at many different frequencies. GDY uses a modal superposition technique to calculate the dynamic response where the total response is considered as the sum of the response of the various individual modes of the structure. This is very efficient, but requires that sufficient modes have been included so that the modal model is an accurate representation of the actual structure. How can you determine that enough modes have been included to ensure that the results are accurate?

The table of modal participation factors. The totals exceed 90% in all directions, indicating that the results should be accurate.

One way to do this is to look at the modal participation factor, which can be obtained using the report command after a frequency analysis. If the sum of all the modal participation factors exceeds 90%, then the calculated dynamic response is likely to be accurate.

What is the modal participation factor? When a structure is vibrating, each mode participates in the vibration to some extent. The modal participation factor indicates how much each mode participates in the response and is calculated for translation in the x, y, and z directions, as well as for rotation around those axes. For instance, a given mode may have significant participation in the x direction, but have very little participation in the other directions. How many modes should be included? Theoretically, the sum of all the modal participation factors should be 100%. However, to reach 100%, an infinite number of modes is required. The more modes that are calculated, the closer the sum will be to 100%, but the computer time required to calculate these modes will be greater. Therefore, you want to calculate enough modes so that the sum of the modal participation in all six directions is over 90%. This normally ensures that the results are accurate without the computer time being excessive.

A good starting point is to determine the maximum frequency of loading and then to calculate the modes with natural frequencies up to 2-3 times the maximum loading frequency. You can then look at the list of modal participation factors to ensure that the sum on each direction is more than 90%.

The harmonic analysis of a stiffened panel from an aircraft subjected to white noise. This simulation investigates the response of the panel at frequencies from 100 Hz to 750 Hz to ensure that dynamic effects will not cause fatigue problems in service. In this case, modes with natural frequencies from 0 Hz to 1.5 kHz have been included in the calculation (two times the highest frequency of interest).

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