The vibration generated in vehicles from motors, road conditions, or from rocket and jet engines is a combination of many frequencies and has a certain random nature. Random vibration (modal superposition) analysis determines how the structure of an object or a supported object reacts to constant, random vibration.
Random vibration (modal superposition) analysis uses input from linear natural frequency (modal) analysis and power spectral density curves. They are representations of vibration frequencies and energy in a statistical form. The analysis determines the root-mean-square response of displacement and stress resulting from constant, random vibration over time.
This information can help discern the structural integrity of a vehicle and the effects of vibration on payloads transported by a vehicle.
Random vibration analysis is applicable to excitations, either power spectral densities (PSD) or cross spectral densities (CSD), with a zero mean value. The output is the root mean square response (RMS), and the results are relative to the input excitation.
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Keep in mind that random vibration is a statistical analysis; it is not a deterministic analysis where loads are expressed through known forcing functions. Also, since the input has a zero mean, the mean response is also zero. Therefore, the root mean square of the displacements or stresses is equal to the standard deviation. So, all the results of a random vibration analysis are the standard deviation of the results and not the actual results. For example, the displacement result which can be viewed in the Results environment is the standard deviation of the displacements; they are not the actual displacements.
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Random vibration (modal superpositon) uses the results from a modal analysis and operating systems create files with different formats. So, you must perform the modal analysis and random vibration analysis on the same operating system. (Technically, the endian determines the file format. Any combination of operating systems using the same endian can be used for both analyses.)
The general steps in performing a random vibration analysis are as follows:
- Set up the model for a Natural Frequency (Modal) analysis or Natural Frequency (Modal) with Load Stiffening. The calculated mode shapes are combined during the random vibration analysis. The number of frequencies calculated in the modal analysis should be sufficient to excite the model in the appropriate directions. (Generally, the cumulative mass in the excited directions should be above a certain percentage, such as 80% although design codes can dictate a different minimum.)
- Run the natural frequency (modal) analysis.
- Copy the model to a new design scenario. Right-click the current design scenario heading in the tree view and select Copy.
- Change the analysis type of the new design scenario to random vibration. (Analysis
Change Type Linear Random Vibration) - Enter the power spectrum density (PSD) and parameters in the Analysis Parameters dialog box.
- Indicate which design scenario has the modal results.
- Specify the PSD and directions. The PSD load is transmitted to the model through the appropriate boundary conditions. (PSD in the X direction is transmitted through any boundary conditions that have X translation fixed, and so on.)
- Other types of loads applied to the model have no affect on the analysis.
- Perform the analysis (Analysis Analysis Run Simulation).
- When the analysis is complete, review the results in the Results environment. Use the Results Options Analysis Specific Resultant to toggle between the resultant and the response to each natural frequency. Use the Results Options Load Case Options Load Case to view the response at each natural frequency. Keep in mind that the displacement results are relative to the ground excitation (input spectrum).