Analysis Case Data - Power Spectral Density Form

Access the Analysis Case Data - Power Spectral Density form as follows:

Click the Define menu > Analysis Cases command to display the Analysis Cases form.
Click the Add New Case button or highlight a previously defined analysis case and click the Add Copy of Case or the Modify/Show Case button to display the Analysis Case Data form.
Select Power Spectral from the Analysis Case Type drop-down list to display the Analysis Case Data - Power Spectral Density form.

The Analysis Case Data - Power Spectral Density form is used to view and change the definition of a power-spectral-density (PSD) analysis case. A PSD analysis case solves for the response of the structure resulting from cyclic (harmonic, sinusoidal) loading over a range of frequencies, and then integrates the resulting spectrum weighted by a probabilistic power-spectral-density function to get a root-mean-square (RMS) expected response. The structure may be damped or undamped. Frequency-dependent stiffness and damping (complex impedance) properties may be included for the Link elements.

Important: In a single PSD analysis case you may apply one or more loads at the same or different phase angles. All loads applied in the same analysis case are assumed to be fully correlated, i.e., they are algebraically added.

To do this, each applied load is multiplied by its specified scale factor and the square-root of the specified power-spectral-density function, applied to the structure at its specified phase angle, and summed with all the other loads, similarly applied. The response to this combined load is squared to generate the power-spectral-density response, which can be integrated to get the RMS response. You may also plot the power-spectral density function for any response quantity.

To combine uncorrelated loads, use SRSS type Combinations of PSD analysis cases. The result will be a single RMS value for each response quantity.

For example, consider two uncorrelated machines vibrating on the same platform. Each machine may generate a horizontal X and a vertical Z force, 90 degrees out of phase with each other. The two forces for a given machine are fully correlated since they are both generated by the same eccentric, spinning mass. This problem requires the following:

Four load cases, two directions of force each for two different machines. Call them Machine1X, Machine1Z, Machine2X, and Machine2Z.
Two analysis cases, one for each machine. For machine 1, define a PSD case (call it Machine1) that applies load case Machine1X at a phase angle zero and load case Machine1Z at a phase angle of 90 degrees. Both load cases would typically be scaled by the same power-spectral-density function. Define a similar analysis case for Machine 2.
One Combination. Define an SRSS-type combination of the two analysis cases, Machine1 and Machine2.

Use the various options available on the Analysis Case Data - Power Spectral Density form to solve this and other similar problems.

Stiffness to Use options. Choose whether to solve for the response using the stiffness of the unstressed structure (Zero Initial Conditions - Unstressed State), or at the end of a nonlinear static or nonlinear direct-integration time-history analysis case (Stiffness at End of Nonlinear Case). See Stiffness to Use for more information. If you are uncertain about which option to use, choose Zero Initial Conditions.
Load Applied options. Use the drop-down lists and edit boxes in this area of the form to apply the loads from one or more load cases or built-in acceleration loads, each scaled by the same or different power-spectral-density functions. All specified loads will be added and applied in combination. The loads are fully correlated. To combine uncorrelated loads, define separate PSD analysis cases and combine the results using SRSS-type Combinations.

Load Type drop-down list. Choose whether the load to be applied is a load case or a built-in acceleration load.
Load Name drop-down list. Choose the load case name, or the direction of ground acceleration, depending on the type of load. For acceleration loads, choose direction U1, U2, or U3. See Applying Acceleration Loads for more information.
Function drop-down list. Select the name of a previously defined power-spectral-density function that specifies the square of the magnitude of the load as a function of frequency. The square-root of this function will be used for combining loads in this analysis case. The default unit function, UNIFPSD, is a unit scale factor at all frequencies, corresponding to a uniform probability distribution.
Scale Factor edit box. Enter a scale factor that multiplies the load before adding it to other loads applied. For acceleration loads, the scale factor has units of acceleration, and should be consistent with the length units currently in use. For load cases, the scale factor is unitless. Note that this scale factor is applied to the square-root of the specified power-spectral-density function.
Show Advanced Load Parameters. Check this box to reveal the following additional load application options.

Phase Angle edit box. The phase angle specifies when during a loading cycle the load acts. The loading cycle starts at zero degrees, and repeats every 360 degrees. The load varies during the loading cycle according to cosine(angle – phase), where angle is the current angle in the loading cycle, and phase is the specified phase angle. Thus loading starting at a phase angle of zero follows the cosine function, and loading with a phase angle of 90 follows the sine function.
Coordinate System drop-down list. Specify a coordinate system in which the acceleration directions are measured. See Applying Acceleration Loads for more information.
Angle edit box. Specify an angle by which U1 and U2 are rotated from UX and UY in the specified coordinate system. See Applying Acceleration Loads for more information.

Add button. To add a load to the set of applied loads, specify the load type, load name, and other parameters using the drop-down lists and edit boxes, then click the Add button.
Modify button. To modify a load in the set of applied loads, click on the load in the table to select it, make any changes to the load type, load name, and other parameters using the drop-down lists and edit boxes, then click the Modify button.
Delete button. To remove a load from the set of applied loads, click on the load in the table to select it, then click the Delete button.
First and Last Frequencies. Specify the first (lowest) and last (highest) frequency of the range for which the response is to be calculated and integrated. These two values may not be equal. You may specify additional frequencies of interest using the parameters below. A separate solution will be obtained at each frequency. Frequency values are given in Hz (cycles per second).
Number of Increments. Specify the number of uniformly spaced frequency increments between the first and last frequency at which the response is to be calculated. The increment in frequency is given by the difference between the last and first frequencies, divided by the number of increments. The integrated RMS results may depend on the number of increments. Try several analyses with increasing number of increments until convergent results are obtained.
Set Additional Frequencies button. Click the Set Additional Frequencies button to specify other frequencies of interest that cannot be given as uniform increments. See Additional Frequencies for more information.
Hysteretic Damping. Click the Modify/Show button to access the Hysteretic Damping form and specify the damping to use for the analysis.