Frequency Response

Frequency response (modal superposition) analysis determines the steady-state operation of a machine, vehicle or process equipment design subjected to continuous harmonic loading. As compared to linear transient stress analyses, frequency response (modal superposition) analysis provides an easy, quick method in which the only inputs are a constant frequency and amplitude.


The analysis determines stress, displacement and the phase angle at each mode along with a square-root-sum-of-the-squares response based on steady-state inputs.


For example, this analysis type could be used to determine the vibration effects of a washing machine with an unbalanced load or a bent wheel on a vehicle.



Since frequency response (modal superpositon) uses the results from a modal analysis, and since operating systems create files with different formats, both the modal analysis and frequency response analysis need to be performed 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 frequency response analysis are as follows:

  1. Set up the model for a Natural Frequency (Modal) analysis or Natural Frequency (Modal) with Load Stiffening. The calculated mode shapes will be combined during the frequency response analysis, so 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 may dictate a different minimum.)

  2. Run the natural frequency (modal) analysis.

  3. While reviewing the natural frequency results, find the node numbers where the harmonic loads are desired. (This step can be skipped if the load is a ground motion load, in which case the load is automatically applied through the boundary conditions.)

  4. Copy the model to a new design scenario. (Right-click on the current design scenario heading in the tree view and choose "Copy".)

  5. Change the analysis type of the new design scenario to frequency response. ("Analysis: Analysis Type: Linear: Frequency Response")

  6. Enter the harmonic loads and parameters in the Analysis Parameters dialog ("Analysis: Parameters...").

    1. Indicate which design scenario has the modal results.

    2. Specify the forcing frequencies, directions, and nodes at which the loads act.

    3. Other types of loads applied to the model have no affect on the analysis.

  7. Perform the analysis ("Analysis: Perform Analysis...").

  8. When the analysis is complete, review the results in the Results environment. Use the "Results Options: Response Type" menu to toggle between the in-phase, out-of-phase, and SRSS response to each natural frequency. Use the "Results Options: Load Case" menu to view the response at each natural frequency. When using ground acceleration, keep in mind that the displacement results are relative to the ground excitation.