Configuring a mode-based steady-state dynamic analysis

You can configure a mode-based steady-state dynamic analysis to calculate the steady-state dynamic linearized response of a system to harmonic excitation. Abaqus/Standard calculates the response based on the system's eigenfrequencies and modes, which must first be extracted by using the eigenfrequency extraction procedure (described in Configuring a frequency procedure”). This type of procedure is computationally cheaper than direct-solution or subspace-based steady-state analysis, but is less accurate, in particular if significant material damping is present. For more information, see Mode-Based Steady-State Dynamic Analysis.

This task shows you how to:

Create or edit a mode-based steady-state dynamic procedure

  1. Display the Edit Step dialog box following the procedure outlined in Creating a step (Procedure type: Linear perturbation; Steady-state dynamics, Modal), or Editing a step.
  2. On the Basic and Damping tabbed pages, configure settings such as frequency range and damping definitions as described in the following procedures.

Configure settings on the Basic tabbed page

  1. In the Edit Step dialog box, display the Basic tabbed page.
  2. In the Description field, enter a short description of the analysis step. Abaqus stores the text that you enter in the output database, and the text is displayed in the state block by the Visualization module.
  3. Choose a Scale option to indicate whether you want the frequency range(s) of interest to be divided using a Logarithmic or Linear scale.
  4. Toggle on Use eigenfrequencies to subdivide each frequency range if you want the frequency range(s) of interest to be subdivided using the system's eigenfrequencies. For more information, see Selecting the Type of Frequency Interval for Which Output Is Requested.
  5. Enter the following data in the Data table:

    Lower Frequency

    The lower limit of the frequency range or a single frequency, in cycles/time.

    Upper Frequency

    The upper limit of the frequency range, in cycles/time. If you enter zero, Abaqus/Standard assumes that results are required only at the frequency specified in the Lower Frequency column.

    Number of Points

    The number of points in the frequency range at which results should be given.

    If you toggled on Use eigenfrequencies to subdivide each frequency range, this is the number of points at which results should be given, including the end points, from the lower limit of the frequency range to the first eigenfrequency in the range; in each interval from eigenfrequency to eigenfrequency; and from the highest eigenfrequency in the range to the high limit of the frequency range.

    If you toggled off Use eigenfrequencies to subdivide each frequency range, this is the total number of points in the frequency range, including the end points.

    Bias

    The bias parameter. This parameter is useful only if you request results at 4 or more frequency points. It is used to bias the results points toward the ends of the intervals so that better resolution is obtained there. This option is recommended if you have toggled on Use eigenfrequencies to subdivide each frequency range, since the ends of each interval are the eigenfrequencies where the response amplitudes vary most rapidly.

    For more information, see The Bias Parameter.

    For detailed information on how to enter data, see Entering tabular data.

Configure settings on the Damping tabbed page

  1. In the Edit Step dialog box, display the Damping tabbed page.

    (For information on displaying the Edit Step dialog box, see Creating a step, or Editing a step.)

  2. Indicate how you want to provide damping values:

    • Choose Specify damping over ranges of Modes to provide damping values for specific mode ranges.

    • Choose Specify damping over ranges of Frequencies to provide damping values at specific frequencies. Abaqus/Standard interpolates the damping coefficient for a mode linearly between the specified frequencies

    If you omit damping data on the Damping tabbed page, Abaqus/Standard assumes zero damping values. For more information, see Specifying Modal Damping.

  3. If you selected Modes in Step 2, select one or more of the following options for defining damping:

    • Display the Direct modal tabbed page to specify the fraction of critical damping, ξ, for a particular mode range. Do the following:

      1. Toggle on Use direct damping data.

      2. Enter the following in the data table:

        • Start Mode: the mode number of the lowest mode of a range.

        • End Mode: the mode number of the highest mode of a range.

        • Critical Damping Fraction: fraction of critical damping, ξ.

    • Display the Composite modal tabbed page to select composite modal damping using the damping coefficients calculated in the preceding frequency step. (The damping calculations performed in the frequency step are performed using damping data provided in the material definition). Do the following:

      1. Toggle on Use composite damping data.

      2. Enter the following in the data table:

        • Start Mode: the mode number of the lowest mode of a range.

        • End Mode: the mode number of the highest mode of a range.

    • Display the Rayleigh tabbed page to define Rayleigh damping, and do the following:

      1. Toggle on Use Rayleigh damping data.

      2. Enter the following in the data table:

        • Start Mode: the mode number of the lowest mode of a range.

        • End Mode: the mode number of the highest mode of a range.

        • Alpha: mass proportional damping, αM.

        • Beta: stiffness proportional damping, βM.

    • Display the Structural tabbed page to define damping that is proportional to the internal forces but opposite in direction to the velocity. Do the following:

      1. Toggle on Use structural damping data.

      2. Enter the following in the data table:

        • Start Mode: the mode number of the lowest mode of a range.

        • End Mode: the mode number of the highest mode of a range.

        • Damping Constant: Damping factor, s.

    For detailed information on how to enter data, see Entering tabular data.

  4. If you selected Frequencies in Step 2, select one or more of the following options for defining damping:

    • Display the Direct modal tabbed page to specify the fraction of critical damping, ξ, for a particular frequency range. Do the following:

      1. Toggle on Use direct damping data.

      2. Enter the following in the data table:

        • Frequency: frequency value in cycles/time.

        • Critical Damping Fraction: fraction of critical damping, ξ.

    • Display the Rayleigh tabbed page to define Rayleigh damping, and do the following:

      1. Toggle on Use Rayleigh damping data.

      2. Enter the following in the data table:

        • Frequency: frequency value in cycles/time.

        • Alpha: mass proportional damping, αM.

        • Beta: stiffness proportional damping, βM.

    • Display the Structural tabbed page to define damping that is proportional to the internal forces but opposite in direction to the velocity. Do the following:

      1. Toggle on Use structural damping data.

      2. Enter the following in the data table:

        • Frequency: frequency value in cycles/time.

        • Damping Constant: Damping factor, s.

    For detailed information on how to enter data, see Entering tabular data.

  5. If desired, repeat Steps 2–4 to create multiple damping definitions.

When you have finished configuring settings for the step, click OK to close the Edit Step dialog box.