Glossary term

Shock Response Spectrum

Maximum response of a family of single-degree-of-freedom oscillators to a transient shock input, used to compare equipment shock severity across natural frequency.

Branch: Mechanical Engineering
Glossary type: method
Content: Glossary term
Updated: Jun 25, 2026
Revision: v1.0.1 · reviewed

Definition

method

A shock response spectrum is a plot of the maximum response of many single-degree-of-freedom oscillators when they are subjected to the same transient shock input.

In shock qualification and transient structural dynamics, the input time history is applied to an oscillator bank with different natural frequencies and a stated damping ratio. The largest absolute acceleration, relative displacement, pseudo-velocity or pseudo-acceleration reached by each oscillator is then plotted against natural frequency. The result compares shock severity by dynamic response, not by FFT amplitude alone.

A shock response spectrum, often abbreviated SRS, describes how severe a transient shock is for structures with different natural frequencies. The shock time history is applied to a family of single-degree-of-freedom oscillators. For each oscillator, the maximum response is recorded and plotted against natural frequency.

For base acceleration input, a common oscillator equation is:

m\ddot{u}+c\dot{u}+ku=-m\ddot{y}(t)

where $u(t)$ is relative displacement, $y(t)$ is base displacement, $m$ is mass, $c$ is damping and $k$ is stiffness. Each oscillator has:

\displaystyle \omega_n=\sqrt{\frac{k}{m}}, \quad f_n=\frac{\omega_n}{2\pi}

and a stated damping ratio:

\displaystyle \zeta=\frac{c}{2m\omega_n}

The SRS ordinate must state what maximum response is being plotted. Common choices are maximum absolute acceleration, maximum relative displacement, pseudo-velocity and pseudo-acceleration. If $D$ is the maximum relative displacement response, then:

PV=\omega_nD

and:

PA=\omega_n^2D

These pseudo quantities are oscillator-equivalent response measures. They are useful for comparing shock severity, but they are not a replacement for the measured time history when phase, pulse timing, sign, fatigue cycles or detailed load paths matter.

Engineering Role

Shock response spectra are used when engineers need to compare transient shock environments against equipment fragility, qualification limits, spacecraft launch environments, drop shock, transport shock, pyrotechnic events, seismic equipment response, impact events or fixture-induced transient loads.

The method is valuable because a short shock pulse can be harmless for one structure and damaging for another. A component with a natural frequency near a strong SRS ordinate may amplify response even if the input pulse is brief. A much stiffer or much softer component may see a different maximum acceleration, displacement or stress.

An SRS helps answer practical questions:

which natural-frequency bands are most severe for this shock;
whether a mounted component has force, acceleration or clearance margin;
whether a test fixture is overtesting or undertesting a frequency band;
whether a simulated shock envelope covers the measured environment;
which damping value, axis, polarity and response quantity were used for acceptance.

The damping ratio is part of the specification. A 5 percent damped acceleration SRS and a 2 percent damped acceleration SRS are different acceptance curves. Positive and negative SRS traces may also be different when the shock pulse is asymmetric.

Measurement Chain and Conventions

An SRS is only as credible as the shock time history used to compute it. The measurement record should preserve the shock pulse, avoid clipping, sample fast enough for the highest required oscillator frequencies and document any baseline correction or filtering. The Nyquist limit is:

\displaystyle f_N=\frac{f_s}{2}

but a practical SRS calculation usually needs margin below Nyquist because filtering, sensor bandwidth, numerical integration and fixture resonances can distort high-frequency response before the formal sampling limit is reached.

The report must also state whether it is plotting positive, negative or maximax SRS, and whether the ordinate is absolute acceleration, relative displacement, pseudo-velocity or pseudo-acceleration. These curves can have the same frequency axis while answering different engineering questions. A pseudo-acceleration ordinate is useful for force screening, while relative displacement can be more relevant for clearances, connector strain or isolator stroke.

Worked Example: Screen a Mounted Electronics Module

A small electronics module is reviewed against a qualification shock response spectrum. The module has:

m=2.50\ \text{kg}

Its first local mounted mode is estimated at:

f_n=80\ \text{Hz}

The 5 percent damped SRS report gives a pseudo-acceleration ordinate at that frequency:

PA=25g

Convert the pseudo-acceleration to SI units:

PA=25(9.81)=245.25\ \text{m}/\text{s}^2

A first-pass inertial-force estimate is:

F_{pk}=mPA=2.50(245.25)=613\ \text{N}

If the mount force allowable is $900\ \text{N}$ , the force margin is:

\displaystyle \text{margin}=\frac{900}{613}=1.47

The force screen appears acceptable. Now check clearance. The circular natural frequency is:

\omega_n=2\pi f_n=2\pi(80)=502.65\ \text{rad}/\text{s}

For a pseudo-acceleration SRS ordinate:

\displaystyle D=\frac{PA}{\omega_n^2}

so:

\displaystyle D=\frac{245.25}{502.65^2}=9.71\times10^{-4}\ \text{m}=0.971\ \text{mm}

The available internal clearance is:

c_{clear}=0.60\ \text{mm}

The displacement demand ratio is:

\displaystyle \frac{D}{c_{clear}}=\frac{0.971}{0.60}=1.62

Engineering comment: the mount force has a margin of about 1.47, but the pseudo-displacement screen exceeds the available clearance by about 62 percent. The result does not prove that contact will occur in the real assembly, because SRS does not retain phase, sign, pulse sequence or multi-mode coupling. It is strong evidence that the design needs a detailed time-domain model, a measured mode check, more clearance, a different mount or a revised shock isolation strategy before release.

Shock response spectrum is not base excitation. Base excitation is the support-motion input condition. SRS is a response summary computed from a transient input.

Shock response spectrum is not transmissibility. Transmissibility is an output/input ratio for a specified dynamic system, often in steady-state harmonic analysis. SRS records maximum oscillator response to a transient event across natural frequency.

Shock response spectrum is not a Fourier spectrum. An FFT shows frequency content in the input or response signal. SRS shows peak response of oscillators and discards phase and time ordering.

Shock response spectrum is not a waterfall spectrum. A waterfall stacks spectra across time, speed or operating condition. SRS sweeps oscillator natural frequency for one shock record or envelope.

Shock response spectrum is not modal testing. Modal tests identify natural frequencies, mode shapes and damping. SRS uses assumed oscillator properties to characterize a shock environment or acceptance envelope.

Shock response spectrum is not a complete stress analysis. It can screen frequencies, accelerations and pseudo-displacements, but detailed stress, connector load, solder-joint strain, clearance impact and fatigue assessment may require time-domain simulation or test correlation.

Validation and Common Mistakes

A defensible SRS calculation states the input time history, axis, polarity convention, damping ratio, response quantity, oscillator frequency spacing, sample rate, anti-alias filtering, baseline correction, integration method, fixture location and whether the curve is measured, enveloped, synthesized or required by specification.

Common mistakes include:

comparing a 2 percent damped SRS with a 5 percent damped requirement;
treating pseudo-velocity or pseudo-acceleration as directly measured velocity or acceleration;
reading an SRS as if it retained phase, duration or pulse order;
using a low sample rate that aliases high-frequency shock content;
ignoring fixture resonances and sensor mounting response;
applying one-axis SRS results to a different structural axis;
accepting a shock test because the input SRS passes while the unit response, clearances or local strain are not measured;
using an SRS envelope for fatigue without checking time history, cycle count and damage equivalence.

SRS is strongest as a shock-severity and qualification-screening tool. It becomes an engineering decision only after the response quantity, damping, frequency band, measurement quality and design failure modes are tied to the component being assessed.

REF

Disciplines

Shock Response Spectrum

Definition

Engineering Role

Measurement Chain and Conventions

Worked Example: Screen a Mounted Electronics Module

Validation and Common Mistakes

See also

Engineering Role

Measurement Chain and Conventions

Worked Example: Screen a Mounted Electronics Module

Distinction from Related Terms

Validation and Common Mistakes