SUMMARY
When analyzing structural or mechanical systems subjected to dynamic loading, one of the most important considerations is how the system dissipates energy—this is where damping comes into play. Often, we simplify our models using constant damping across all modes, but in reality, damping behavior can vary significantly from one mode to another.
In this article, we explore how to implement mode-dependent damping in a modal superposition harmonic response analysis using ANSYS. This approach provides more realistic and accurate dynamic response predictions, especially when higher modes start to dominate. Let’s walk through the procedure step-by-step, explaining both the method and the reasoning behind each step.
Step 1: Create a Damped Modal Analysis
The first step is to perform a damped modal analysis. This analysis serves a specific purpose: to extract the damping ratio for each mode. Instead of applying a constant damping ratio, we can define damping as a function of frequency using a damping stress coefficient or a user-defined expression. This results in a non-uniform damping distribution across the modal spectrum. For this example, a constant damping stiffness factor do the work.
Step 2: Duplicate the Modal Analysis and Set It to Undamped
Once the damped modal analysis is complete, the next step is to create an undamped version of the same analysis. This can be done by duplicating the initial setup and simply setting the “Damped” option to “No”.
This undamped modal analysis is required as the foundation for the Harmonic Response Analysis. This is because ANSYS’s modal superposition method—used in harmonic analysis—does not support results from a damped modal solver. Instead, damping must be defined explicitly within the harmonic analysis setup, using methods such as APDL commands. Therefore, even if damping is considered in a preliminary modal analysis for evaluation, the actual modal basis used in the harmonic step must be undamped.
Observation: Mode frequencies will shift slightly between damped and undamped analyses. This is expected and reflects how damping affects the natural frequencies.
Step 3: Setup the Harmonic Analysis
With the undamped modal results available, you can now proceed to create a Harmonic Response Analysis. This is where you simulate how your structure responds to sinusoidal excitation across a range of frequencies.
In the harmonic setup:
1. Link the undamped modal results as the base for the mode shapes and frequencies.
2. Set all global damping values to zero in the Harmonic settings. This avoids introducing uniform damping across all modes.
3. Instead, apply damping through a more refined approach: an APDL snippet using the MDAMP command.
Step 4: Use the MDAMP Command for Mode-Dependent Damping
The MDAMP command in ANSYS APDL lets you define damping ratios mode-by-mode, providing much greater control. It works by specifying the starting mode and then up to six damping values for subsequent modes. This command is very simple, the initial mode number and then up to six damping ratio values for the next modes. If more than six modes are needed, use an additional MDAMP command starting at the 7th mode.
This example sets damping ratios from modes 1 to 6. These values should be extracted from the earlier damped modal analysis, allowing the harmonic response to reflect the true energy dissipation behavior of the system.
Note: If you accidentally define a non-zero value in the Harmonic Analysis damping field, that value will be added on top of the MDAMP results as a uniform damping value. Avoid this to preserve mode-dependent behavior.
Step 5: Interpret Harmonic Results
Once the harmonic analysis is complete, plotting the frequency response gives a clear visual comparison of how damping affects your system.
You can compare three cases:
1. Mode-dependent damping (blue curve): This is the most accurate representation, as it reflects realistic damping variations across modes.
2. Constant damping (orange curve): Created using a uniform damping value equal to the first mode’s ratio. As expected, it matches the mode-dependent case near the first natural frequency, but diverges at higher frequencies.
3. Undamped model (green crosses): A useful reference to observe how damping suppresses resonance and affects the amplitude at various frequencies.
This comparison highlights how critical it is to account for damping variation across modes. Uniform damping may provide a good approximation for the first few modes but fails to capture the system’s true behavior at higher frequencies.
Conclusion
By combining a damped modal analysis, an undamped modal model, and custom APDL damping definitions using MDAMP, you can create a harmonic response analysis with realistic, mode-dependent damping. This method leads to more reliable predictions for dynamic systems, especially those with complex modal behavior.
Whether you're working in aerospace, automotive, or industrial equipment design, incorporating realistic damping models is a best practice you shouldn't overlook.
💡 Final Thought: Don’t settle for average when analyzing dynamic systems. Mode-dependent damping is a small step with a big payoff in accuracy.
Ozen Engineering Expertise
Ozen Engineering Inc. leverages it's extensive consulting expertise in CFD, FEA, thermal, optics, photonics, and electromagnetic simulations to achieve exceptional results across various engineering projects, addressing complex challenges like multiphase flows, erosion modeling, and channel flows using Ansys software.
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