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# Comparing Sierra SM Explicit Transient to Direct and Modal FRF

Example files on this page

- Cantilever Beam FRF example problem — Salinas_rtest/training/exampleproblem/frf/direct/smFRFcomp/beam_frf.e

- directFRF — Salinas_rtest/training/exampleproblem/frf/direct/smFRFcomp/frf_dir.inp

- modalFRF — Salinas_rtest/training/exampleproblem/frf/direct/smFRFcomp/frf_m.inp

- Sierra/SM explicit transient — Salinas_rtest/training/exampleproblem/frf/direct/smFRFcomp/beam_sm.i

# 4. Comparing Sierra SM Explicit Transient to Direct and Modal FRF

FRFs are a matrix of relationships from forced input to either displacement, velocity, or acceleration output. Typically, system response is accessed using acceleration.

Frequency Response Functions. The transfer function \([H]\) relates the force input to the displacement between two points in the system. The transfer function is symmetric and is formed as a function of mass, damping, and stiffness. The transfer function is differentiable and the relationship of the force to the acceleration is shown using the following in matrix form:

\[ \bar{A} = \ddot{[H]} \bar{F} \]

More information can be found in the theory manual.

Mesh. Figure 4.1 shows a sample mesh that was used both as an input for Sierra/SD Modal and Direct FRF as well as for the Sierra Solid Mechanics Code - Adagio. The Node where force is applied is connected to the beam using a network of rigid Rbars and the force is applied in the Z-direction.

Figure 4.1 Cantilever Beam FRF example problem

Three inputs are considered: modalFRF, directFRF, and Sierra/SM explicit transient.

The input below shows the relevant portions of the direct FRF input file. The keyword `alpha = 5` sets the mass damping of the system. The `frequency` section has the frequency range from .1-50Hz at .1Hz increments. A general rule of thumb is that the highest frequency mode requested in the `solution` section should be at least 1.5x the max frequency in the `frequency` section.

    LOADS
     nodeset 500
     force = 0 0 1
     scale = 1
     function = 1
    END

    FUNCTION 1
      type LINEAR
      name "white noise"
      data 0.0 1.0
      data 200. 1.0
    END

    DAMPING
     alpha = 5
    END

    FREQUENCY
      freq_min = .1
      freq_step = .1
      freq_max = 50
      acceleration
      disp
      nodeset 2
    END

Figure 4.2 FRF Z-axis Modes ResultsAcceleration of end node in the Z-axis direction.

Figure 4.2 compares modal and direct FRF with the same damping. There are enough modes for the modal FRF to show nearly exact agreement to the direct frf results. Each of the frequencies used for the adagio input show reasonable agreement. The discrepancies seen are possibly due to the possibility that the alpha damping in adagio is not one-to-one related to the alpha damping in Sierra/SD.

Table 4.1 shows each method’s run time. A caveat should be noted here that 10 cycles were used in the Adagio input to ensure that the system reached steady state. Reducing the number of cycles reduces the run time proportionally. In addition, with complex systems, eigen solution run time added to the modal FRF solver time may approach the direct FRF solution time. It also should be noted that Adagio run was performed with the knowledge of mode frequency locations. If it were not, it is possible that the frequencies needed to plot would be closer together and more numerous.

Table 4.1 Run Times (min:sec).
Method | Time
--- | ---
Modal FRF (20 modes) | 00:09
Direct FRF | 02:41
Sierra SM (8 frequencies) | 129:48