Jet noise is an acoustic excitation that applies random pressure loading to the surface of a structure. The pressure at a point is assumed to have a power spectral density , where is frequency, measured in cycles per time. For this case, following Olson, we assume that the excitation is white noise (1.0 at all frequencies) and that the acoustic waves are traveling along the structure with a velocity (where is taken to be 6.0 in this case). The cross-spectral density of the pressure loading between any two points can then be written as

where is the distance between the two points for which is being given. This type of loading is specified by using the TYPE=MOVING NOISE parameter provided in the *CORRELATION option for random response analysis. The *CORRELATION option acts between loads applied at the nodes of the model. In this case, since the elements are all of equal length, a load of magnitude 0.25 is applied equally to all nodes to simulate the pressure loading. Thus, has only the discrete values of the distance between any combination of two nodes. Olson points out that this approximation reduces the accuracy of the results unless a rather fine mesh is used. However, the mesh used here provides results that agree well with those of Olson up to relatively high frequencies, suggesting that the approximation is not too coarse.

For purposes of illustration we also show input data for the case where we apply the loading via user subroutines UPSD and UCORR. These subroutines allow the user to define a different frequency dependence and magnitude for each entry in the cross spectral density matrix. Any number of frequency functions can be used to define the cross spectral density of the loading as

where is a complex frequency function defined in the *PSD-DEFINITION option and referenced in the th *CORRELATION option, is the corresponding th correlation matrix for load case for degrees of freedom at node and at node , and is the load applied to degree of freedom at node in load case . Since there are 21 nodes in our model and the elements are all of equal length, the construction of can be accomplished as follows. Concentrated nodal loads of 0.25 (corresponding to the length of each element) are applied to all of the nodes. In user subroutine UPSD we specify 21 complex frequency functions, each for a particular value of , the distance between two nodes and is equal to 1.0 (white noise) in this case. These frequency functions are referenced in 21 *CORRELATION options in the *RANDOM RESPONSE step. For each of these options matrices are defined in user subroutine UCORR, each with unity in the appropriate positions and zero elsewhere.