SRS Analysis
FEA LEARNING CENTER
Shock Response Spectrum
The Frequency Fingerprint of a Shock
By Joseph P. McFadden Sr.
McFaddenCAE.com
Companion document to the FEA Learning Center
in the Abaqus INP Comprehensive Analyzer
Imagine you have a piano, and you slam the lid shut.
Every string in that piano will respond — but not equally. The strings whose natural frequencies align with the energy content of that slam will vibrate strongly. Strings tuned to frequencies where the slam had little energy will barely move. If you could measure the peak response of every string, you'd have a map showing which frequencies the slam excited most and which it didn't.
That map is essentially a shock response spectrum.
The SRS doesn't describe the shock itself. It describes how a family of single-degree-of-freedom systems — imagine thousands of tiny spring-mass oscillators, each tuned to a different natural frequency — would respond to that shock. It translates a time-domain event into a frequency-domain representation of its damage potential.
And that makes it one of the most powerful tools in structural dynamics — when you understand what it's actually telling you.
The Why — What The Srs Gives You That Peak G Doesn't
A shock pulse has a peak acceleration. It has a duration. But what it does to your structure depends on where the energy falls in frequency — and that's invisible if all you look at is the time-domain waveform.
Two pulses can have identical peak G and identical duration but very different SRS curves. A sharp, spiky pulse concentrates energy at high frequencies. A smooth, slow pulse concentrates energy at low frequencies. Your structure doesn't care about the shape of the pulse in time. It cares about how much energy arrives at its natural frequencies.
The SRS reveals exactly that. At each frequency on the x-axis, the SRS tells you the peak response — acceleration, velocity, or displacement — of an oscillator tuned to that frequency. If your circuit board has a natural frequency of 800 Hertz and the SRS shows a peak at 800 Hertz, that board is going to be excited heavily. If the SRS has a valley at 800 Hertz, the board may be fine even though the overall pulse is severe.
This is why qualification standards specify environments in terms of SRS rather than time-domain pulses. NASA, military standards, and commercial test specifications define the shock environment as an SRS curve — a spectrum that your product must survive. The test laboratory generates a transient shock that meets or exceeds that SRS at every frequency. The specific time-domain shape doesn't matter. What matters is that the frequency content covers the specification.
The What — How Srs Is Computed
The computation is conceptually simple. You take your acceleration time history — from a test measurement or from a simulation — and you feed it through a bank of single-degree-of-freedom oscillators. Each oscillator has a different natural frequency. For each oscillator, you record the peak response. Plot peak response versus natural frequency, and you have your SRS.
The Q factor — amplification factor — determines how much each oscillator amplifies at its resonance. Higher Q means less damping, sharper resonance, higher peak response. Q of 10 is the standard assumption for most structural analyses, corresponding to 5 percent critical damping. But your actual structure may have more or less damping, so it's important to report what Q factor was used. The SRS at Q of 10 and the SRS at Q of 50 look very different — same shock, very different response amplitudes.
There are multiple types of SRS. The maximax SRS takes the absolute peak response regardless of sign — this is the most common and most conservative. The primary SRS looks only at the response during the shock pulse itself. The residual SRS looks at the free vibration after the pulse ends. For qualification purposes, the maximax SRS is standard.
And there's a subtle but important variant — the pseudo-velocity SRS. Instead of plotting peak acceleration, it plots peak velocity response. This matters because pseudo-velocity is directly proportional to strain energy in the oscillator. A pseudo-velocity SRS gives you a direct picture of the damage potential across frequency. Two shocks with identical acceleration SRS curves but different velocity SRS curves can cause very different levels of strain and fatigue damage. The acceleration SRS tells you about peak force. The velocity SRS tells you about stored energy. Both are important.
The How — Srs Analysis In Abaqus
In Abaqus, SRS analysis is a two-step procedure.
Step one is a modal analysis — frequency extraction. You extract the natural frequencies and mode shapes of your structure. Everything we discussed in the modal analysis Learning Center script applies here: density must be defined, boundary conditions must be correct, enough modes must be extracted to cover the SRS frequency range, and — critically — no contact elements.
Step two is the response spectrum step. You define the SRS input — frequency versus acceleration, typically from a specification or test measurement — specify the damping, and the solver computes the peak response in each mode. The results are then combined using a combination rule — SRSS (square root of the sum of the squares), absolute sum, or NRL (Naval Research Laboratory) grouping. The choice of combination rule affects the conservatism of the result. SRSS is standard for well-separated modes. If modes are closely spaced, NRL grouping or absolute sum may be more appropriate.
The critical limitation — and I'll say this every time because it's that important — SRS analysis in Abaqus is a perturbation procedure. Contact elements cannot be used. This is non-negotiable. If your structure has contact interfaces — bolted joints, press fits, gasket connections — those must be modeled as tied constraints or merged nodes. Contact is state-dependent stiffness. Perturbation procedures require constant stiffness. The two are incompatible.
Material nonlinearity is also excluded. If the actual shock is severe enough to cause yielding, the linear perturbation SRS analysis won't capture that. It will overpredict the response at yielding locations because it doesn't account for the energy absorbed by plastic deformation. For those cases, you need a full transient dynamic analysis in the time domain.
Practical Wisdom
Here are the things that separate a credible SRS analysis from a box-checking exercise.
Extract enough modes. If your SRS specification goes to 2,000 Hertz, extract modes up to at least 4,000 Hertz. Modes above the SRS range still contribute to quasi-static response. Cutting them off too early underestimates the total response.
Check participation factors. If the cumulative effective mass in your excitation direction is less than 85 to 90 percent of total mass, extract more modes. Missing mass means missing response.
Use the right damping. If you have test data, derive the damping from half-power bandwidth measurements. If you don't, Q of 10 is a reasonable default for assembled structures with bolted joints. For machined monolithic parts with minimal joints, Q of 25 or higher may be more realistic — and more conservative, since less damping means higher peak response.
Understand the limitations of the results. SRS analysis gives you peak response — the maximum stress, displacement, or acceleration — but not the time history. You don't get to see the dynamic animation the way you do with a transient analysis. You get the envelope of worst-case response across all modes combined. That's powerful for qualification — pass or fail — but less useful for debugging a failure mechanism.
And when you compare SRS analysis to test data, remember that the SRS itself is computed from a measured acceleration time history. The quality of that acceleration measurement — sensor mounting, filtering, sampling rate, signal conditioning — directly affects the SRS. A poorly mounted accelerometer can produce an SRS that's wrong by a factor of two or more. If your simulation doesn't match the test SRS, the test measurement is worth questioning too.
The Connection
SRS analysis sits at the intersection of modal analysis and shock. It takes the frequency-domain foundation that modal analysis provides and applies the energy content of a shock event through it. It's elegant, efficient, and — for a wide range of qualification problems — sufficient.
But when it's not sufficient — when contact matters, when materials yield, when you need the time history rather than just the peak — you need to cross into explicit dynamics and run the full transient analysis. Both tools belong in your toolkit. The skill is knowing which one to reach for.
DSP tools for computing SRS from test data and simulation output — including the Smallwood ramp-invariant algorithm, pseudo-velocity computation, and multi-parameter fragility assessment — are available at McFaddenCAE.com.
This has been a Learning Center discussion on the shock response spectrum. I'm Joe McFadden. Thanks for listening.
About the Author
Joseph P. McFadden Sr. is a CAE engineer specializing in finite element analysis, modal analysis, materials behavior, and injection mold tooling validation. With nearly four decades of experience in structural simulation, he brings a holistic perspective to engineering education — connecting how systems respond to how people think and learn.
His work at McFaddenCAE.com includes the Abaqus INP Comprehensive Analyzer — a desktop tool for analyzing, visualizing, and extracting sub-assemblies from large FEA models without requiring an Abaqus license — along with DSP tools for SRS computation, jerk extraction, velocity change analysis, and energy balance verification.
The FEA Learning Center is an integrated educational platform within the Analyzer, providing guided discussions on structural dynamics topics with working example INP files. This document series is the companion written reference for those discussions.
The four-volume FEA Best Practices audiobook series — Building the Model, The System's Natural Character, When Things Collide, and Keeping the Simulation Honest — is available at McFaddenCAE.com.
