SigFit allows the user to compute the rigid-body motions, changes in radius-of-curvature, and RMS errors of optical surfaces due to three types of dynamic loads: transient, harmonic, and random. While transient and harmonic response results from a NASTRAN finite element analysis may be processed as part of the standard polynomial fitting routine, the advanced dynamics capabilities in most codes are often optional features. Furthermore, quantities such as surface RMS error and change in radius-of-curvature cannot be computed within the random response capabilities of the finite element codes supported by SigFit. SigFit uses modal techniques for all three types of analyses for which the only finite element results required are the modeshapes and corresponding natural frequencies to be included in the analysis. To illustrate these capabilities, results are shown for the primary mirror of the telescope model shown in Figure 1.

Transient Response
Responses of optical surfaces due to time dependent loads are computed by SigFit using modal transient analysis. The time dependent load definition is entered in two parts. The first part defines the magnitude of the load as a function of space while the second part defines the magnitude as a function of time. The product of the two definitions is the resulting load used in the analysis. The spatial dependence may be entered manually or by reading an MSC/NASTRAN OLOAD definition in PUNCH file format.

The time dependence may be entered manually as load magnitude vs. time data. SigFit can also automatically generate this time dependence for constant and sinusoidal loads. Results are given in the ASCII output file as a list of optical surface rigid-body motions, change in radius-of-curvature, and surface RMS error at each time requested.

The time step and duration used in the analysis is user controllable as well as the times at which results are printed. This allows the user complete control to choose enough time steps for the transient analysis calculations while limiting the results to only what is needed.

Harmonic Response
Harmonic responses of optical surfaces due to tonal inputs may be computed with modal harmonic analysis. The loaded nodes, directions, and magnitudes are specified by the user in the same manner as is done for transient analysis.

The frequency range, frequency step, and number of extra frequencies to be evaluated near the natural frequencies are entered by the user. The user may also manually enter a frequency variation to the harmonic loads in either linear-linear or log-log format.

The output of the harmonic analysis, as shown in the truncated output list (Table 1), is given in the ASCII output file as a list of optical surface rigid-body motions, change in radius-of-curvature, and surface RMS error at each forcing frequency.

Table 1

Random Response
With an input power spectral density SigFit can compute the random response of optical surfaces. The loaded nodes are defined as is done for transient and harmonic analyses described above. The power spectral density break points can be input manually in either linear-linear or log-log form.

The output of the random analysis includes the response power spectral densities of optical surface rigid-body motions, change in radius-of-curvature, and surface RMS error given in the ASCII output file. A truncated example is listed in Table 2 and plotted in Figure 3.

Table 2

As an aid to performing design trades, SigFit lists the percent contribution of each dynamic mode to the overal response power spectral density for each result type. This listing aids the user in understanding which modes require attention in order to improve the system’s performance. An example listing is shown in Table 3.

Table 3

The data in Table 3 indicates that in order to reduce the surface RMS error of the primary mirror, efforts should be concentrated on reducing the response of modes 5 and 29.

SigFit’s random response results output concludes with a random response summary giving the 1 sigma and 3 sigma limits on response for each response type. The zero crossings and 1 sigma acceleration are recorded as well.

Table 4