DADiSP Software Modules
Spectrum SRS Tutorial
SRS Introduction
The Shock Response Spectrum, or SRS, is used in modeling a mechanical component as a series of
spring-dashpot subsystems each with a constant damping ratio and varying natural frequency.
Each spring-dashpot subsystem is considered a 2nd order linear system and is converted into the digital
domain. The absolute maximum response of each spring-dashpot subsystem is returned as the SRS result for
the corresponding natural frequency of the subsystem. A plot of the absolute maximum responses for all
the natural frequencies is the Shock Response Spectrum.
Basics:
After the DADiSP/SRS Module is installed, an SRS button will appear in the toolbar of DADiSP as shown in Figure 1.
Figure 1
By selecting the SRS button in the DADiSP toolbar, the SRS menu will open as in Figure 2.
Figure 2
Discussion of Features:
As previously mentioned, each spring-dashpot subsystem is converted into the digital domain. The Method
option in the SRS menu determines how each subsystem is converted into the digital domain. The following
three options are available: The Impulse Invariant technique matches the impulse response of the analog
system with the digital model; The Ramp Invariant (Smallwood) technique, which is the most common approach,
matches the ramp response of the analog system with the digital model; and the Bilinear Transform matches
the frequency responses.
Two options are available for the spacing of natural frequencies in the resulting SRS plot: 1/N Fractional
Octave frequency spacing from minimum to maximum frequency (N = 1 for whole octave spacing); and Linear
frequency spacing from minimum to maximum frequency.
Additional options include the number of Natural Frequencies per Octave (the value for N when Frequency
Spacing is 1/N Octave) or number of Total Natural Frequencies (used when Frequency Spacing is Linear),
Minimum and Maximum Natural Frequencies, Damping Factor (equivalent to 1/Q Factor) or Q Factor (equivalent
to 1/Damping Factor).
Exercise 1:
The following exercise will demonstrate how to perform a simple SRS analysis on shock data (acceleration time
history data) as in figure 3.
Figure 3
The shock data shown in Figure 3 was loaded into W1 of the worksheet. The data was sampled at 500 kHz for
about 0.25 seconds resulting in 125,000 samples. The data ranges from approximately -7.9 to 8.4 G's.
To aid in determining the minimum and maximum frequencies for use in the SRS Menu, the SPECTRUM function
within DADiSP can be utilized to display the frequency content of the data. To access the SPECTRUM
function menu, select the fx button in the DADiSP toolbar to open the Function Wizard as shown in Figure 4.
Figure 4
Select "FFT/Spectral" in the Analysis Category, select "Spectrum" in the Function Name list and then press the
OK button on the Function Wizard menu. The Spectrum menu will open as in figure 5.
Figure 5
Set the options in the Spectrum menu to the following specifications and press OK button:
| Input series:
|
W1 |
| Windowing function: |
Hamming |
| Length: |
Best power of 2 |
| Windowing correction factor: |
Amplitude |
| Remove dc offset: |
Checked |
| Destination: |
W2 |
The spectrum of the shock data will display in W2 as shown in figure 6. Window 2 ha been set to display
the x-axis in log format. By visual inspection of the spectrum plot, determine the minimum and maximum
relevant frequency values to be used in the SRS menu.
Figure 6
This example will demonstrate how to perform the SRS using the Smallwood method. Press the SRS button on
the DADiSP toolbar. The SRS menu will open and make the appropriate changes as in figure 7:
Figure 7
After entering the following specification, press the OK button in the SRS menu. The results will display
in W3 as shown in Figure 8. Note the maximum frequency for this example was set at 250KHz to show the
entire natural frequency range.
| Method: |
Ramp invariant (smallwood) |
| Frequency spacing: |
1/N octave |
| Freq. per octave: |
6 |
| Min frequency: |
1 |
| Min frequency: |
250000.0 |
| Damping factor: |
0.05 |
| Q factor: |
20 |
| Destination: |
W3 |
Figure 8
Summary
Mechanical components used in industries such as Aerospace Engineering, Automotive Engineering, and
Defense can often encounter shock from variety of sources. Engineers must design and test these components
to guarantee reliability. Ultimately, SRS analysis will help minimize the potential damage to a component
due to shock.
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