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Obtain shock response spectrum (SRS) by applying the acquired shock pulse to a series of single degree of freedom (SDOF) systems. Plot the system maximum response as resonance frequency of the system.

An SDOF mechanical system consists of the following components:

• Mass, whose value is represented with the variable m
• Spring, whose stiffness is represented with the variable k
• Damper, whose damping coefficient is represented with the variable c

The resonance frequency, f_N, and the critical damping factor, ζ, characterize a SDOF system, where:

For light damping where ζ is less than or equal to 0.05, the peak value of the frequency response occurs in the immediate vicinity of f_N and is given by the following equation, where Q is the resonant gain:

The following front panel illustrates the response of a SDOF system to a half-sine pulse with a 10 g acceleration amplitude and 10 ms duration.

The top graph shows the time-domain acceleration. The middle graph is the SDOF system response with a 50 Hz resonance frequency. The bottom graph is the SDOF system response with a 150 Hz resonance frequency. In both cases, ζ is 0.05.

Use the signals shown in the previous front panel to construct the SRS. For example, the maximax, the absolute maximum response of the calculated shock response signal over the entire signal duration, uses the absolute maximum system response as a function of the system natural frequency. The following front panel illustrates the maximax SRS for the same half-sine pulse.

Note  Each computed SRS is specific to the pulse used to perform the measurement.

You can use other types of shock spectra depending on the application. These spectra include the initial shock response from the system response over the pulse duration or from the residual shock spectrum of the system response after the pulse. You can use the positive maximum, the negative maximum, or the absolute maximum response signal value.

The NI Sound and Vibration Measurement Suite uses the Smallwood algorithm to compute the SRS. The SVT Shock Response Spectrum VI also provides the ability to preprocess the time-domain signal to improve SRS results. You can remove any DC component or apply a lowpass filter with a selectable cut-off frequency.

The SVT Shock Response Spectrum VI can compute the SRS from the absolute acceleration response or from the relative displacement response. Use the model control on the SVT Shock Response Spectrum VI to select the appropriate response.

The following block diagram shows an example of using the SVT Shock Response Spectrum VI.

The example in the previous block diagram acquires 1,000 samples of data from an accelerometer during a shock. The shock signal triggers the acquisition. The example stores 100 samples before the trigger to capture the entire shock signal.

The following front panel displays the acquired time-domain signal and the computed SRS.