Harmonic analysis is a technique used to determine the steady-state response of linear structures to loads that vary sinusoidally (harmonically) with time. In harmonic analysis, the entire structure has constant or frequency-dependent stiffness, damping and mass effects. The structure’s response at several frequencies is calculated to obtain a graph of some response quantity (usually displacements) versus frequency. Thereafter, peak responses are identified and stresses reviewed at those peak frequencies.
Harmonic analysis can be solved either using full harmonic or mode-superposition techniques each with advantages and disadvantages as shown here.
| The Full Method | The Mode-Superposition Method |
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Base Excitation in Harmonic Analysis
Base excitation is commonly used in the world of vibration testing where shaker tables drive a structure sinusoidally through a range of frequencies at known amplitude and phase. In ANSYS Mechanical with ANSYS Workbench, harmonic acceleration can be applied using three different techniques.
Global Support Acceleration Method “GSAM”
In the global support acceleration method GSAM, the entire structure is subject to acceleration as a global excitation. Although this is the most straightforward method to apply a base acceleration, the output does not resemble the actual testing environment since it only reports the relative motion between the base and the rest of the structure (i.e., the base is already fixed). Also, phase information is lost in this case.
This global acceleration is applied using the ACEL command that does not support frequency dependent acceleration.
Large Mass Method “LMM”
LMM is another old technique that was introduced to account for the major drawback of the GSAM (i.e., it gives an absolute output). The LMM is an approximate technique that treats the response to acceleration excitation as a response to external forces. The base excitation is simulated by rigidly attaching a very large mass “M” to the support base of the structure. A force equals to Mass*Acceleration (F = Ma) is then applied to the point of the mass in the excitation direction. This method gives a good approximation, but it requires using command snippets in ANSYS Mechanical.
Enforced Motion Method “EMM”
The EMM is a newly developed technique in ANSYS V14.5. This method allows you to apply base excitation (displacement or acceleration). Excitation can be either constant or time/frequency dependent. This method overcomes all the above-mentioned drawbacks because it accounts for the phase difference and the relative motion. It also allows for a non-constant excitation.
Below is a summary of a recently developed ACT extension that implements the EMM in ANSYS Mechanical. An example of a sizing deck that is shacked using a constant harmonic base acceleration of 10 g in the z direction is illustrated.
Figure 1: A sizing deck geometry model.
Model setup:
Figure 2: Harmonic analysis using linked Modal Analysis system
In the Modal Analysis:
In the Modal Analysis you define a named selection for all support bases in the model. Note that if multiple excitation locations exist for the same model, a unique named selection has to be assigned for each of the supports.
Create Base:
- Select a base named selection.
- Define excitation direction.
- Give the base a unique integer ID number.
Figure 3: Base definition in modal analysis
In the Harmonic Analysis branch:
- Acceleration or displacement base excitation can be added.
- The loading can be either constant or frequency-dependent.
Figure 4: Excitation application in Mode-Sup Harmonic analysis
Plotting the average vertical deformation, over frequency, of the table-top as well as the base is shown below. As it can be seen in Figure 6 and Figure 7, the support of the sizing deck has a non-zero displacement calculated as Acceleration/Frequency^2.
Figure 5: Table top deformation, Uz, frequency response
Figure 6: Base deformation, Uz, frequency response
Figure 7: Vertical deformation at around resonance
Below, Figure 8 shows a comparison between the Global Support Acceleration Method, the Enforced Motion Method, and the Large Mass Method. As you can see, the GSAM technique is under-estimating the deformation at low frequency, whereas it overestimates the deformation at higher high frequencies. The reason for such a behavior is that GSAM does not account for the phase difference between the base and the table top as seen in Figure 9.
Figure 8: Frequency response (table deformation) comparison between EMM, LMM and GSAM
Figure 9: Deformation at F = 150Hz (GSAM vs EMM)
In conclusion, there are three different techniques that can be used to harmonically excite a base of a structure. At first glance, applying a direct acceleration appears to be the most straightforward technique. However, it lacks some phase information since the base of the structure is fixed. As an alternative, the old technique of Large Mass can be utilized, but it requires the use of command snippets in ANSYS Mechanical.
A more convenient, yet simple to implement, technique is the Enforced Motion Method: an ACT extension that allows applying an acceleration or displacement base excitation. This method overcomes the disadvantages of the direct acceleration technique.
Thanks, that looks very useful. Will the extension be uploaded to the Customer Portal?
Yes, the extension will be uploaded soon to the portal.
That is really an useful new feature for customers, And now they often use BIG MASS METHOD, and that is not comfortable in workbench