Prosig Shock Response Analysis

In aerospace and nuclear applications, the failure of electronic components due to mechanical shock is often more difficult to detect than structural failure. These shocks may result from a series of relatively low-level impacts or a single high-energy event. The relationship between a shock event and its potential to cause damage is complex, and direct measurement is not always practical or cost-effective.

To address this challenge and ensure the reliability of shock-sensitive components, the Shock Response Spectrum (SRS) has been widely adopted across multiple industries as a low-cost and practical shock simulation and evaluation technique.

A leading UK science and technology centre in the space sector selected Prosig’s advanced SRS module to evaluate the damage potential of spacecraft components. The SRS analysis was used to support laboratory-based design improvements for spacecraft and avionics systems, ensuring components can withstand expected shock environments and maintain reliable performance.

The Prosig SRS module provides an intuitive interface that allows users to compute the SRS by specifying frequency step size and damping factor. It also supports multiple combinations of primary, residual, and composite SRS calculations, enabling detailed analysis of system response under different excitation phases. The module incorporates an optimised SRS algorithm developed by Prosig engineers to deliver high computational efficiency and accurate results.

What is SRS Analysis:

In laboratory testing, resonant test fixtures are often excited using air guns or other mechanical impact sources (such as pendulum systems, pneumatically driven pistons, or free-fall masses). A test item mounted to the fixture is subjected both to direct shock input and to the resonant response of the fixture, simulating a pyroshock environment.

Shock Response Spectrum (SRS) analysis decomposes the system into a set of independent single-degree-of-freedom (SDOF) mass–spring–damper subsystems, each defined by a specific natural frequency and damping ratio. The peak response of each subsystem is extracted as a function of its natural frequency. The resulting spectrum, representing maximum response versus frequency, is known as the SRS.

To compute the SRS, consider a set of linear damped SDOF subsystems with natural frequencies , mounted on a fixed base (Figure 1).

Figure 1 Sketch of illustrating the subsystem

The governing equation of motion for a nth sub-system is

…Equ.(1).

where and represent the absolute acceleration of nth subsystem and the base. are the mass, viscous damping ratio and stiffness of the nth subsystem. These inertia quantities can be expressed by nth subsystem’s natural frequency and structural damping loss factor

…Equ.(2)

…Equ.(3)

Note here is often represented by the Q factor, where Q=1/(2). Q=10 is commonly used for pyro-sock testing

Substituting Equ. (2) and Equ. (3) into and Equ. (1), the analytical solution to Equ.(1) was derived in Irvine’s work as

…Equ(4)

Here, the acceleration level, , is measured using accelerometers attached to the test specimen. The natural frequency and damping ratio are user-defined parameters. The resulting subsystem acceleration can therefore be computed numerically. The full SRS workflow is illustrated in Figure 2.

Base Shock Response []

The measured base acceleration is obtained from accelerometers mounted on the test setup, as shown in Figure 2.

The overall response is typically divided into two phases:

Primary event: The period during which the transient excitation is applied (typically < 20 ms)
Residual event: The response after the excitation has ceased

SRS analysis may be performed on the primary event, residual event, or the complete time history.

SRS Time History Analysis [(]

Shock signals typically contain high-frequency content with high acceleration levels but relatively low velocity and displacement amplitudes. Pyroshock frequency content generally ranges from 100 Hz to 10,000 Hz or higher.

The frequency range and spacing define the number of SDOF subsystems used in the analysis. Both linear and octave spacing may be applied. Once natural frequencies

chosen and damping ratios are defined, each subsystem response is computed using Eq. (4).

SRS Analysis [Max( ]

Prosig SRS module supports computation of primary, residual, and composite spectra using selectable frequency steps/octave, damping factors, and algorithms.

Users may also select absolute, positive, or negative spectra. Three algorithms are available within DATS: Smallwood, Land, and Mercer/Lincoln, each employing different coefficient formulations in recursive computation.

Using the Mercer/Lincoln implementation, SRS outputs can be represented in terms of acceleration, velocity, or displacement (Figures 3–5).

Shock spectral analysis is then used to evaluate the maximum response of each subsystem under shock loading, enabling engineers to assess damage potential and verify compliance with test specifications.

An example SRS calculation worksheet is shown in Figure 6.

SRS Application Cases:

Application 1: Shock Response Analysis

The SRS method is widely used to characterise transportation and operational environments. For example, MIL-STD-810 defines crash hazard shock response spectra for selected equipment. This can be used to ensure that a radio installed in a military vehicle remains operational following a moderate collision.

NASA-STD-7003A provides standardised requirements for developing pyroshock test criteria for spacecraft, payloads, and launch vehicle hardware. The standard defines qualification margins, acceptance criteria, and verification procedures. Pyroshock environments are typically externally induced; therefore, assembly-level qualification is often performed using simulated shock sources incorporating a 3 dB margin above the maximum expected flight environment.

Standards such as MIL-STD-1540 and MIL-STD-810 are widely used to define shock environments and qualification procedures across aerospace and defence applications.

Application 2: Shock Response Synthesis

This application enables synthesis of multiple shock environments to form an enveloped damage spectrum representing combined loading conditions.

For example, a vessel at sea may experience both rogue wave impacts and sudden wind gusts. If these events occur independently or simultaneously, the SRS must account for both conditions by enveloping their combined response

In some test specifications, reproducibility of shock inputs is required. DATS software provides a range of shock generation options.

Examples of shocks generated by DATS software.

Application 3: Required Response Spectrum Simulation (RRS)

In certain applications, test requirements specify a Required Response Spectrum (RRS) derived from structural modification effects on mounted components. This approach correlates SRS results with system-level damping variations, such as those introduced by isolators.

By computing SRS across different damping ratios as shown in Figure 10, engineers can evaluate the influence of isolation systems on shock transmission.

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Dr Cindy (Xin) Wang

Applications Engineer at Prosig

Cindy has a BSc from the Dept of Jet Propulsion at Beijing University of Aeronautics and Astronautics, a Masters from the University of Sheffield in Mechanical Engineering and an MPhil/PhD from the University of Southampton for her thesis “Computational aeroacoustics of slat track system”. Cindy has extensive experience working in Automotive and joined Prosig in 2019 as an Applications Engineer.