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Convert a Time History to SRS


Author Tom Roberts

Shock testing is critical when a piece of equipment must survive concussive, sudden impact, or high acceleration events. To test equipment against complex shock events, engineers often employ the shock response spectrum (SRS). The SRS uses a mathematical model to synthesize a shock pulse that simulates a transient event on a shaker.

As with sine and random vibration testing, engineers want their SRS test profile to reflect the field environment as closely as possible. This likeness helps to ensure that test levels are sufficient and there will not be unexpected failures post-production. While synthetic response spectrums are standard, engineers can convert a time-history file to an SRS for a test profile comparable to the field.

Recordings in Place of Synthetic Waveforms

Usually, engineers select a synthetic waveform to synthesize an SRS pulse, and the best choice depends on the application. For example, the burst random and enveloped burst random methods produce long-duration stationary random waveforms suitable for earthquake simulation. However, synthetic waveforms do not closely match real-world transient events.

Fortunately, engineers can modify field recordings to meet or exceed a specified SRS. This approach generates a time waveform like the recorded environment with a similar frequency response function.

Enveloping Recordings

A ‘max enveloping’ waveform overlaid on recorded data

A max enveloped waveform overlaid on recorded data.

This proposed approach incorporates multiple real-world data sets into one representative waveform. Using one shock event to create a synthesized SRS waveform would give an incomplete description of shock vibrations that may occur in the field.

The proper way to combine multiple data sets of transient events is to find the maximum value at each frequency rather than the average acceleration. This “maximum enveloping” technique produces an SRS curve using the maximum acceleration value at each frequency from a group of real-world data sets.

Why Maximum Acceleration?

SRS theoretical diagram

A basic model of the SRS.

The SRS calculation models response channels using a theoretical series of single-degree-of-freedom mass-damper-spring oscillators. The natural frequency of each SDOF oscillator defines the plot’s horizontal axis, and a computed response for each oscillator is on the vertical axis. This computed response is the absolute maximum acceleration of the SDOF oscillator to the pulse, not the average acceleration.

Convert a Time History to SRS

The VibrationVIEW software can implement the max enveloping technique to convert a time-history file to an SRS. It supports SRS iteration to create a waveform that meets or exceeds the SRS maximax breakpoint table values. The following paper makes a compelling case for the new approach.

Improve SRS Test Development


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