Random Vibration
A Random Vibration node () defines a random vibration analysis based on a frequency response reduced-order model, primarily for structural mechanics simulations. This feature makes it possible to postprocess the power spectral density (PSD) of a Frequency Domain, Modal Reduced-Order Model’s response to random loads described by their power spectra. The output is presented using operators like <rom_name>.psd(...), <rom_name>.rms(...), and <rom_name>.cross(...) where <rom_name> is the Name of the Random Vibration node. For details, see Performing a Random Vibration Analysis in the Structural Mechanics Module User’s Guide.
The Settings window for a Random Vibration node contains the following sections:
Frequency Response Model
From the Frequency response model list, choose an existing Frequency Domain, Modal Reduced-Order Model node representing the frequency-domain behavior of the structure.
Power Spectrum
From the Correlation type list, choose a type of correlation: Uncorrelated (the default), Fully correlated, or Cross-correlated. If you choose Cross-correlated, a correlation matrix input appears at the bottom of this section.
For each reduced-order model input used in the selected Frequency response model, and displayed in the Control name list, enter an input Power spectral density expression. Note that this expression is usually a function of the frequency, freq.
If the correlation type was set as Cross-correlated, fill in expressions for the off-diagonal elements of the cross-correlation between the reduced-order model inputs. These expressions are typically frequency dependent and complex-valued.
Output Operator Settings
In this section, you can provide default settings for random vibration operators that perform an integration over the frequency. These operators have two different syntaxes — for example, <rom_name>.rms(expr) and <rom_name>.rms(expr,lower_freq,upper_freq,number_of_points). When the first form is used, the remaining arguments are inferred from the settings in this section.
Enter a Lower frequency limit and an Upper frequency limit as bounds for the integration. Usually, this is the frequency range for which the input PSD is defined. Then, select an Integration method — Automatic or User defined. For both methods, the integration points are distributed logarithmically above the fundamental frequency (the lowest eigenfrequency of the frequency response model) and linearly below it. For User defined, enter the Number of integration points used in the numerical integration. For Automatic, the number of integration points is determined as follows: above the fundamental frequency, 50 integration intervals per decade are used; below the fundamental frequency, the density of integration points is that which the logarithmic distribution gives just above the fundamental frequency.