Hello Everyone
I hope everyone's having a good day. I'm here to talk about random vibration.
Introduction to Random Vibration
Random vibration involves multiple frequencies acting upon a system simultaneously. This is common because, in real-world scenarios, systems or structures often experience a variety of random frequencies at the same time. The unique aspect of random vibration is its statistical nature, which differentiates it from other types of vibration analyses.
Common Applications
- Vehicles on roadways, including freight transportation and vehicle suspension systems.
- Airplanes during operation, such as taxiing, takeoff, and in-flight vibrations from engines and wind resistance.
- Supports for equipment, like HVAC systems on building rooftops, which must withstand operational and wind loads.
- Rocket and spacecraft launches, where vibrations from all components must be analyzed for safety.
Power Spectral Density (PSD)
Power Spectral Density is a method to analyze random vibrations by collecting them into frequency bins and displaying the power density as a root mean square across frequencies. This statistical analysis is quicker than transient analysis and is crucial for understanding system responses to random vibrations.
Frequency Bins
Frequency bins are used to categorize random vibrations. For example, bins might include:
- 0 to 20 Hz
- 20 to 40 Hz
- 40 to 60 Hz
- 60 to 80 Hz
- 80 to 100 Hz
At each frequency, the root mean square is calculated to create a power spectral density.
Analysis Requirements
Random vibration analysis must be linear, meaning the structure cannot have time-varying stiffness, damping, or mass. Boundary conditions must also remain constant.
Loading Random Vibration
Random vibration is loaded using a modal analysis, which can be done by:
- Dragging and dropping random vibration separately and connecting them individually.
- Dragging and dropping random vibration directly onto the solution node of a modal analysis.
Pre-stressing, such as from a pre-tensioned bolt, should be applied before the modal analysis and then fed into the random vibration analysis.
Statistical Analysis
Random vibration is analyzed statistically using a Gaussian curve. ANSYS allows for calculations at different sigma levels:
- 1 sigma (68.27% of total response)
- 2 sigma (95.45% of total response)
- 3 sigma (99.73% of total response)
Example: Truss Design
In this example, a simple truss design is analyzed using modal analysis. Areas of concern are identified in different mode shapes, guiding the random vibration analysis.
Applying PSD Acceleration
PSD acceleration can be derived from acceleration data or standards. In ANSYS, data reliability is indicated by line colors:
- Green: Reliable
- Yellow: Potentially okay
- Red: Unreliable
ANSYS can subdivide yellow or red lines into green segments for improved accuracy using the "improved fit" option.
Post-Processing
Directional deformation post-processing provides maximum deformation in the Y-axis for different sigma levels. A response PSD tool can be used to analyze specific points, providing insights into local responses and aiding further analysis, such as fatigue analysis.
Conclusion
Random vibration analysis is a crucial tool in engineering, providing insights into how systems respond to complex, simultaneous frequency inputs. By using statistical methods and tools like ANSYS, engineers can ensure the reliability and safety of structures and devices under random vibration conditions.
For more information, please contact Ozen Engineering, Inc.
Hello everyone, I hope everyone's having a good day. I'm here to talk about random vibration. When dealing with random vibration, multiple frequencies act upon our system simultaneously. This is more statistical of an analysis than other analyses we've presented.
Common applications include vehicles on a roadway, airplanes during operation, supports holding multiple pieces of equipment, and rocket and spacecraft launches.
We can't talk about random vibration without discussing power spectral density (PSD), which displays power density as a root mean square across frequencies. PSD comes from random input, such as shaker table, accelerometer, or raw data.
Frequency bins collect random vibrations, and the root mean square provides the average value. This analysis needs to be linear, meaning the structure will not have random properties. Time-bearing stiffness, damping, or mass will not be included, nor will time-bearing boundary conditions.
For random vibration, we load it using a modal analysis, either by dragging and dropping random vibration separately and connecting them individually or by dragging and dropping random vibration directly onto the solution node of a modal.
Pre-stressing, such as pre-bend or pre-tension, needs to be done before the modal and fed into our modal analysis. The response from random vibration is a statistical variable.
ANSYS allows us to display and calculate 1, 2, or 3 times the root mean square, accounting for 68.27%, 95.45%, and 99.73% of the total response, respectively. In the example, a truss with a modal analysis shows areas of concern in the third and fourth mode shapes.
PSD acceleration is applied to the analysis, and ANSYS deems unreliable data as yellow or red. Improved fit subdivides the distance, frequency, and PSD value into multiple segments for a more accurate result.
A directional deformation post-process provides a maximum directional deformation in the Y-axis for a one sigma probability. A response PSD tool analyzes a single point for acceleration along the Y-axis. The response PSD plot shows the highest response frequency.
This information can be used for fatigue analysis.
