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The Shock Response Spectrum (SRS) is used to characterize transient and shock waveforms in terms of their effect on single degree-of-freedom (DOF) mechanical systems. The SRS calculated from a time waveform can be used to predict the effect of that waveform on more complex, multi-degree-of-freedom structures. Sometimes, it is necessary to generate a waveform with a specified SRS. The SRS Synthesis module generates short, transient time waveforms from a user-defined SRS profile.

Basics of SRS Synthesis

The purpose of Shock Response Spectrum Synthesis is to generate a time domain waveform that meets criteria of Required Response Spectrum, or RRS, defined in the Shock Response Spectrum (SRS) domain.

A sine wave alone will generate an SRS with a sharp peak. To generate a signal with an arbitrary SRS shape defined by the test profile, multiple sine waves can be combined to form a composite waveform.


Figure 1. SRS of a Sine Wave 

SRS Synthesis uses a sequence of sine waves (called wavelets) to generate the time waveform. Generating an SRS from a waveform is not a linear process, and there are potentially many time waveforms that have the same SRS. There is no direct way to calculate a time signal from an SRS. The SRS Synthesis algorithm uses an iterative approach, where multiple wavelets are combined to form a “guess”, and then the resulting SRS is compared to the target profile. The error from this result is then used in generating a new “guess” waveform. This process is repeated until the result converges on the target.


Figure 2. SRS of Multiple Sine Waves

Once we have a collection of wavelets that contain a large enough number of frequencies, the SRS will be controllable to an extent. Changing the amplitude of these sine waves will change the SRS shape. This is the basic mechanism of SRS synthesis.

To illustrate the synthesis process, please refer to the diagram below. First, the user will need to define a RRS, Required Response Spectrum as the target. Then a number of wavelets corresponding to the resonance frequencies of each SDOF filters are defined. The amplitudes of these wavelets can be adjusted so that the shock response spectrum of the synthesized waveform is closed to the RRS. 


Figure 3. SRS Synthesis

Although the synthesized waveform may meet the SRS criteria, it may not meet the requirement of zero ending velocity and zero ending displacement. After the waveform is synthesized, displacement compensation has to be applied to make it suitable for use on a shaker. This will be done by the software automatically.