Random Vibration Above 2000 Hz: Deriving and Verifying an MPE for Engine-Proximate Components

The Problem

Here is a problem that comes up more often than the standards would suggest. An engineer is deriving a random vibration maximum predicted environment (MPE) for launch vehicle components mounted very close to the engines. Accelerometer data from engine test stand and stack tests show significant broadband energy above 2000 Hz, with peaks near 3000 and 5000 Hz that appear to be driven by engine acoustic modes. The stack test results show no meaningful attenuation of that high-frequency energy at the component mounting locations.

The engineer had already done the hard part, which is screening the data before believing it. The noise floor was clean, the sensors and data acquisition units were rated for the frequency range, and the cabling was shielded. Most persuasively, the peaks migrate in frequency during the burn, tracking the acoustic mode curves. A fixed accelerometer-mount resonance does not do that.

Questions:

1. How should the MPE be derived, and where should the upper frequency bound be set?
2. Is there an accepted way to derive an equivalent test spectrum for a shaker facility limited to 2000 Hz?
3. What instrumentation problems could produce false peaks above 2000 Hz?

Here is a reply, with sections added on stress-velocity considerations and on isolation. The first is the piece that most often reframes this problem entirely. The second is the option that is most often dismissed too early.

1. Deriving the MPE and Setting the Upper Frequency Bound

The SMC-S-016 procedure is reasonable. One important statistical detail is that the overlapping one-second windows should first be used to derive one maxi-max spectrum for each burn or test. The population statistics should then be calculated across independent burns or tests. Overlapping windows from a single burn are not independent samples, and treating them as such inflates the apparent sample size and understates the tolerance factor.

SMC-S-016 defines the random vibration MPE as a P95/50 spectrum, evaluated at intervals no greater than one-sixth octave, over a frequency range of at least 20 to 2000 Hz. It also gives the familiar 4.9 dB margin above the log-mean spectrum when a 3 dB test-to-test standard deviation is assumed. Note that the 4.9 dB figure is 1.645 multiplied by an assumed 3 dB standard deviation. It is the large-sample normal tolerance factor. With a small sample, or with a measured dispersion greater than 3 dB, the required margin is larger, not smaller.

Note also that 2000 Hz is a minimum required upper bound in that definition. It is not a mandatory cutoff when credible energy exists above it.

I would therefore maintain two related specifications:

• A full-band environmental MPE, extending through the highest frequency for which the measurement chain is demonstrably valid and for which the component may have meaningful susceptibility.
• A facility-executable random vibration specification, presently limited to 2000 Hz, accompanied by a documented assessment of the omitted high-frequency environment.

The environmental definition should not be truncated simply because the available shaker cannot reproduce it. The upper bound should instead be based on:

• The highest significant physical excitation.
• The calibrated flat-response range of the accelerometer in its actual mounting configuration.
• The analog anti-alias filter and data acquisition bandwidth.
• The natural frequencies and failure mechanisms of the component, circuit boards, connectors and internal parts.

Retain the original narrowband PSDs and spectrograms in addition to the one-sixth octave envelope. The one-sixth octave result is useful for the MPE, but it may obscure the character and bandwidth of the migrating acoustic peaks. A moving peak may be represented better by an enveloping frequency band than by a very narrow fixed-frequency spike.

Finally, distinguish between mechanically transmitted interface acceleration and direct acoustic excitation. A component near the engines receives both. A base-driven shaker test may reproduce the mounting-point acceleration but will not reproduce pressure loading on covers, panels, circuit boards, wiring or other area-sensitive structures.

2. How Severe Is High-Frequency Energy? The Stress-Velocity View

Before deciding how much effort to spend reproducing the 2000 to 5000 Hz environment, it is worth asking a more basic question: how much structural stress does that energy actually represent?

Acceleration is a poor proxy for stress. Velocity is a much better one. For a traveling wave in a uniform rod, the stress is

$$ \sigma = \rho \, c \, v $$

where $\rho$ is the mass density, $c = \sqrt{E/\rho}$ is the speed of sound in the material, and $v$ is the particle velocity. Gaberson and Eshleman generalized this to modal response as

$$ \sigma_{max} = C \, \rho \, c \, v_{max} $$

where $C$ is a constant of order unity that depends on the mode shape and boundary conditions. The remarkable feature of this relationship is that the material properties collapse into a single constant. For aluminum, with $E = 10 \times 10^6$ psi and a weight density of 0.098 lbm/in³, the speed of sound is about 199,000 in/sec and

$$ \rho c \approx 50 \ \text{psi per in/sec} \qquad (13.6 \ \text{MPa per m/sec}) $$

Velocity Content of a Broadband PSD

The velocity power spectral density follows from the acceleration PSD as

$$ G_v(f) = \frac{G_a(f)}{(2\pi f)^2} $$

so that

$$ v_{rms} = \sqrt{ \int_{f_1}^{f_2} \frac{G_a(f)}{(2\pi f)^2} \, df } $$

For a flat acceleration PSD of amplitude $A$ between $f_1$ and $f_2$, this integrates to

$$ v_{rms} = \frac{1}{2\pi} \sqrt{ A \left( \frac{1}{f_1} \mathbin{\color{black}{-}} \frac{1}{f_2} \right) } $$

The $1/f^2$ weighting is severe. Consider a flat 0.1 G²/Hz environment from 20 to 5000 Hz, split at 2000 Hz into the band a conventional shaker can reproduce and the band it cannot.

Band	Accel (GRMS)	% of accel mean-square	Velocity (in/sec RMS)	% of velocity mean-square	Equivalent RMS stress, aluminum (psi)
20 – 2000 Hz	14.1	39.8%	4.32	99.4%	218
2000 – 5000 Hz	17.3	60.2%	0.34	0.6%	17
20 – 5000 Hz total	22.3	100%	4.34	100%	218

This is why an engineer looking only at overall GRMS will conclude that the truncated test is grossly unconservative, while an engineer looking at velocity will conclude that almost nothing has been lost. Both are computing correctly. They are measuring different things, and velocity is the one that tracks stress.

Resonant Response: The Inverse Square Root Rule

The integral above answers the question, “how much of the input energy matters?” It does not answer the different and equally important question, “how severe is this environment for a mode that actually sits at 5000 Hz?” For that, use the Miles relationship. For a single-degree-of-freedom oscillator with natural frequency $f_n$ and amplification factor $Q$ subjected to base excitation, the response acceleration is

$$ a_{rms} = \sqrt{ \frac{\pi}{2} f_n \, Q \, G_a(f_n) } $$

and the relative velocity across the oscillator is approximately

$$ v_{rms} \approx \frac{a_{rms}}{2 \pi f_n} = \frac{1}{2\pi} \sqrt{ \frac{\pi}{2} \cdot \frac{Q \, G_a(f_n)}{f_n} } $$

So for a fixed PSD amplitude and a fixed $Q$, the modal velocity, and hence the modal stress, scales as $1/\sqrt{f_n}$. Taking 0.1 G²/Hz and $Q = 10$:

• A 200 Hz mode responds at 5.45 in/sec RMS, or roughly 274 psi RMS in aluminum.
• A 5000 Hz mode responds at 1.09 in/sec RMS, or roughly 55 psi RMS.

A factor of five, or 14 dB, for the same input PSD level. That is a real reduction, but it is far less dramatic than the $1/f^2$ result above, and the distinction matters. High-frequency energy is not benign for a mode that lives there. It is benign as a contribution to the response of lower-frequency modes.

Fatigue Damage Scaling

Fatigue damage accumulates as stress raised to the fatigue exponent $b$, multiplied by the number of cycles. Cycle count scales with $f_n$ for a fixed exposure duration, so with $\sigma \propto f_n^{-1/2}$,

$$ D \propto \sigma^b \, n \propto f_n^{\,1 – b/2} $$

The table below gives relative damage for equal PSD amplitude, equal $Q$ and equal duration, normalized to a 200 Hz mode.

Natural frequency (Hz)	Relative modal stress	Relative cycle count	Relative damage, b = 4	Relative damage, b = 6.4
200	1.000	1.0	1.000	1.000
500	0.632	2.5	0.400	0.133
1000	0.447	5.0	0.200	0.029
2000	0.316	10.0	0.100	0.0063
3000	0.258	15.0	0.067	0.0026
5000	0.200	25.0	0.040	0.00084

For a typical aluminum exponent of 6.4, a 5000 Hz mode accumulates roughly one part in twelve hundred of the damage of a 200 Hz mode exposed to the same PSD amplitude for the same duration. Even with the conservative Steinberg value of $b = 4$, the ratio is 25 to 1.

What the Stress-Velocity Argument Does Not Excuse

This reasoning is powerful, and for exactly that reason it must be bounded carefully. It supports the conclusion that high-frequency energy contributes little fatigue damage to distributed metallic structure whose stress is governed by modal velocity. It does not support the following:

• Non-fatigue failure modes. Relay and switch chatter, connector fretting, crystal oscillator instability, MEMS device malfunction, optical misalignment and fastener loosening are all driven by acceleration or displacement, not by cumulative stress. None of them care that the velocity content is small.
• Small, stiff parts. The constant $C$ and the stress concentration factor are not the same for a 200 Hz bracket mode and a 5000 Hz local mode in a lead, a solder joint or a thin cover. Comparing the two on equal $C$ is a screening exercise, not a stress analysis.
• Direct acoustic loading. Pressure acting over the area of a panel or circuit board is a different load path than base motion. The velocity weighting says nothing about it.
• Workmanship screening. Part of the purpose of a random vibration test is to precipitate latent defects, and high-frequency content contributes to that regardless of the calculated fatigue index.

Used properly, the stress-velocity argument tells you where to spend your remaining verification budget. It rarely tells you to spend nothing.

3. Representing the Environment With a Shaker Limited to 2000 Hz

I am not aware of a universally accepted method that simply converts all energy above 2000 Hz into additional PSD below 2000 Hz. I would avoid preserving only the omitted overall $G_{rms}$ by increasing the lower-frequency spectrum. As the table above shows, that approach would raise the low-frequency levels by a large factor to compensate for energy that carries almost no stress, severely overtesting the lower-frequency modes while still failing to test the actual high-frequency modes and stress locations.

A response-equivalence approach is nevertheless useful if its limitations are clearly stated. A practical sequence:

1. Calculate the full-band vibration response spectrum (VRS) from the measured environment for a reasonable range of amplification factors.
2. Calculate the full-band fatigue damage spectrum (FDS) using appropriate ranges of $Q$, fatigue exponent and exposure duration.
3. Determine the natural frequencies and transmissibilities of the component, circuit boards and critical internal parts, using a modal survey, low-level sine sweep, finite element model, component response measurements or a combination.
4. Develop a 20 to 2000 Hz PSD that envelopes the relevant VRS and FDS responses for modes that can actually be excited below 2000 Hz.
5. Identify the remaining response or damage above 2000 Hz as a separate qualification risk requiring another verification method.

The VRS is appropriate for comparing RMS response severity. The FDS extends this by including the number of stress cycles and the test duration, although assumptions are required for damping, fatigue exponent and the relationship between oscillator response and local stress. A velocity-based VRS is often more informative than an acceleration-based one for exactly the reasons developed above.

The key limitation is physical rather than statistical: a shaker input ending at 2000 Hz cannot, in a linear system, directly excite a component mode at 3000 or 5000 Hz. Moving the omitted energy downward may reproduce a scalar damage index, but it produces the damage in the wrong mode, at the wrong physical location, and through the wrong failure mechanism.

4. Practical Challenges Above 2000 Hz

Potential problems include:

• Armature, insert-pattern and head expander resonances.
• Fixture bending, torsional and local plate modes.
• Large spatial variations in acceleration over relatively short distances.
• Phase differences between mounting points.
• Local amplification at the control accelerometer that is not representative of the test item interface.
• Control instability, excessive notching or repeated aborts.
• High interface forces associated with small local fixture motions.
• Reduced shaker force capability and increased sensitivity to payload mass and fixture stiffness.
• Accelerometer mounting resonances and base strain sensitivity becoming part of the control problem.

Multiple control or limiting accelerometers may be needed, together with a low-level sine survey of the empty fixture and of the fixture-plus-test-item assembly. Ideally the fixture’s first significant flexible mode is comfortably above the highest controlled test frequency. That requirement is already difficult for a 2000 Hz test and becomes impractical at 3000 to 5000 Hz unless the component and fixture are both very small and very stiff. Force-limited or response-limited control may help, but extensive notching can itself undermine the intended high-frequency qualification.

For these reasons, extending a conventional component random vibration test from 2000 to 5000 Hz is not simply a matter of changing the controller frequency limit. The fixture and shaker dynamics may dominate the test, making it difficult to demonstrate that the required environment was applied uniformly or representatively. An honest test to 2000 Hz, supported by a documented assessment of the omitted band, is usually better engineering than a poorly controlled test to 5000 Hz.

For components with meaningful modes above 2000 Hz, supplemental methods include:

• Reverberant or direct field acoustic testing.
• A small, high-frequency electrodynamic or piezoelectric shaker.
• Board-level or subassembly-level high-frequency testing.
• Testing at a facility with suitable high-frequency capability.
• Qualification using an instrumented engine or stack test article.
• Analysis combined with material, solder joint, connector and component heritage.
• A mechanical shock test designed using response-spectrum and fatigue-equivalence criteria.

If the 3000 and 5000 Hz response is primarily caused by local acoustic pressure rather than by interface motion, an acoustic test is more representative than trying to force equivalence through a 2000 Hz base-shake spectrum.

5. Reducing the Environment: Isolation

Everything above treats the environment as fixed and asks how to verify against it. There is another option, and for engine-proximate components it deserves to be evaluated before the verification program is written rather than after the first test failure: change the environment at the component interface.

Isolation is unusually attractive for this particular problem. The transmissibility of a base-excited isolated mass falls off above its resonance, so an isolation system is most effective exactly where the shaker is least capable and where the measurement chain is least trustworthy. The energy that is hardest to test is the energy that is easiest to remove.

For a single-degree-of-freedom isolator with natural frequency $f_n$, viscous damping ratio $\zeta$ and frequency ratio $r = f/f_n$, the absolute transmissibility is

$$ T(r) = \sqrt{ \frac{1 + (2 \zeta r)^2}{(1 – r^2)^2 + (2 \zeta r)^2} } $$

The table below is computed for a 50 Hz isolation frequency with $\zeta = 0.17$, which corresponds to $Q \approx 3$ and is representative of a wire rope mount.

Frequency (Hz)	$f/f_n$	Transmissibility	dB	Undamped mount, dB
50	1	3.11	+9.9	resonance
500	10	0.0358	−28.9	−39.9
1000	20	0.0172	−35.3	−52.0
2000	40	0.0085	−41.4	−64.1
3000	60	0.0057	−44.9	−71.1
5000	100	0.0034	−49.4	−80.0

Two features of this table are worth dwelling on. The first is the sheer magnitude of the attenuation available in the problem band: 41 dB at 2000 Hz and 49 dB at 5000 Hz. The second is the last column. A lightly damped mount rolls off asymptotically at 12 dB per octave, while a heavily damped mount rolls off at 6 dB per octave, because the $(2 \zeta r)^2$ term in the numerator eventually dominates. High damping therefore costs roughly 30 dB of high-frequency isolation at 5000 Hz. That trade is almost always worth making, because the alternative is a resonant amplification of 10 or 20 and a relative displacement to match, but it should be made knowingly rather than by default.

Note also that a 50 Hz mount places the isolator resonance near the bottom of the 20 to 2000 Hz specification band. Check what the measured PSD is actually doing between 30 and 80 Hz before committing to that frequency, and coordinate with the coupled-loads analysis, since a 50 Hz rigid-body mode is low enough to interact with vehicle structural modes rather than being safely decoupled from them.

Where the Energy Goes

Apply this to the flat 0.1 G²/Hz environment used earlier. The Miles response of the isolated mass is

$$ a_{rms} = \sqrt{ \frac{\pi}{2} f_n \, Q \, G_a(f_n) } = \sqrt{ \frac{\pi}{2} (50)(3)(0.1) } = 4.85 \ \text{GRMS} $$

Numerical integration of $T^2(f) \, G_a(f)$ over 20 to 5000 Hz gives 4.85 GRMS as well. The resonance dominates so completely that the Miles estimate and the full integration agree to three figures. Against 22.3 GRMS unisolated, that is a 13.3 dB reduction in overall level.

Now apply the velocity criterion from Section 2. The isolated response velocity is approximately $a_{rms} / (2 \pi f_n)$, or about 6.0 in/sec. The unisolated environment was 4.34 in/sec. By the velocity measure, isolation has apparently made the situation worse.

That comparison is wrong, and the reason it is wrong is instructive.

This is also why the isolator frequency must be chosen with the component’s internal modes in view, not merely to obtain a large number in a transmissibility table. Place $f_n$ well below the first significant elastic mode of the component and its circuit boards. Then confirm that the input PSD does not have a peak sitting at $f_n$, because the isolator will amplify whatever is there by a factor of about three.

Relative Displacement and Sway Space

The displacement has to go somewhere, and it goes across the mount. For base excitation the relative displacement is approximately

$$ Z_{rms} \approx \frac{a_{rms}}{(2 \pi f_n)^2} $$

For the case above, $Z_{rms} \approx 0.019$ inch, or about 0.057 inch at three sigma. That is manageable. The random environment is rarely what sizes the mount. The transients are. An ignition or shutdown transient, a stage separation event or a pyrotechnic shock producing an SRS of 100 G at 50 Hz implies a relative displacement of

$$ Z = \frac{(100)(386)}{(2 \pi \cdot 50)^2} \approx 0.39 \ \text{inch} $$

That is the number that drives the hardware selection. Four tenths of an inch of single-event stroke, in all six degrees of freedom, plus margin for the random superimposed on it, plus harness service loops, is a real packaging constraint that has to be negotiated early. It is also the requirement that rules out most compact elastomeric mounts, and the reason a wire rope isolator becomes the practical choice at this frequency.

Why Wire Rope Isolators

For a component mounted near the engines, the two governing constraints are usually temperature and stroke, and those two together tend to eliminate elastomers.

• Temperature. A wire rope isolator is entirely metallic: stranded stainless steel cable threaded through aluminum or steel retainer bars. There is no elastomer to stiffen at low temperature, soften at high temperature, take a compression set, creep under sustained preload, or change its loss factor by a factor of several across the mission profile. Base heating, plume radiation and soakback near the engine compartment are exactly the conditions under which a silicone or fluoroelastomer mount’s published dynamic properties stop applying.
• Stroke. Wire rope mounts accommodate large relative displacements, with a softening characteristic in compression and roll that helps limit transmitted force during transients. This is the property that lets one mount handle both the sustained random environment and the shock environment.
• Damping. Energy dissipation comes from Coulomb friction between the individual strands. It requires no fluid, no viscoelastic layer and no temperature-compensated design. Typical effective damping ratios are 0.15 to 0.20.
• Environmental durability. No outgassing, no ozone or ultraviolet degradation, no radiation aging, no shelf life. Useful for long-duration or reusable hardware.

The cost of these properties is that a wire rope isolator is frankly nonlinear. Its stiffness is amplitude dependent and softens as the excitation grows, so the natural frequency measured during a low-level sine survey will be higher than the natural frequency exhibited at full test level. The damping is hysteretic rather than viscous, so the equivalent $\zeta$ is itself amplitude dependent. Characterize the mount at the amplitude of interest and treat the linear transmissibility above as a design estimate, not as a prediction.

What Defeats an Isolation System

Isolation systems fail in service for a small number of recurring reasons, and almost none of them are the isolator’s fault.

• The harness. A stiff cable bundle, coaxial line, waveguide, fluid line or grounding strap that bridges the isolator short-circuits it. This is the single most common reason a correctly designed isolation system does not work in flight. Provide generous service loops, route them so that they are compliant in all six directions, and measure the installed transmissibility with the flight harness in place rather than with the bench harness.
• Six modes, not one. An isolated component has three translational and three rotational rigid-body modes. Center-of-gravity offset from the plane of the mounts couples them, and wire rope stiffness differs substantially among the tension-compression, roll and shear axes. Verify all six by modal survey.
• Minimum stiffness requirements. Many programs impose a minimum first-mode frequency on installed equipment. An isolation system violates it by design. That conflict has to be resolved with the loads and coupled-loads groups, not discovered at the design review.
• Bottoming. An isolator driven past its stroke into a snubber or a structural stop generates its own high-frequency shock, which is precisely the environment the isolator was installed to remove. Size the sway space for the transients, not for the random.
• Thermal path. A mount that isolates vibration may also isolate the conduction path to the heat sink. Coordinate with thermal early.
• Quasi-static loads. The mounts carry steady and low-frequency inertial loading in addition to the vibration. Check that the preload and the steady deflection leave adequate remaining stroke.

The Effect on the Verification Program

If isolators are used, the component qualification environment becomes the isolated response, not the interface environment. Derive it by applying the measured or tested transmissibility to the full-band MPE, and re-run the VRS and FDS comparisons against the isolated spectrum. In many engine-proximate cases this collapses the entire problem: the 3000 and 5000 Hz content is attenuated by 45 to 50 dB, falls below the noise of the qualification spectrum, and a conventional 20 to 2000 Hz test becomes fully representative.

Two cautions. Qualify the isolator itself over the full temperature range and the full-band input, since the mount sees the unattenuated environment even if the component does not. And note that isolation addresses base motion only. It does nothing about direct acoustic pressure acting on the component’s covers and panels, which remains an argument for an acoustic test where the pressure field is significant.

6. A Shock Test as Supplemental Coverage

It may be possible to show that a suitably designed shock test covers the omitted environment above 2000 Hz. A shock transient contains broadband frequency content and can excite component modes well above the upper frequency of a conventional random vibration test.

Calculate the shock response spectrum (SRS) of the measured engine environment, or of representative time history segments, and compare it with the SRS of the proposed shock test. The shock test could be considered adequate for peak response if its positive and negative SRS envelope the maximum expected response over the critical frequency range, including the 3000 and 5000 Hz regions.

The SRS alone, however, addresses only the maximum response of each single-degree-of-freedom oscillator. It does not account for duration, number of cycles or cumulative fatigue damage. A single high-level shock could envelope the peak response while producing far less fatigue damage than several seconds of sustained random vibration. Evaluate both peak-response equivalence using the SRS and fatigue equivalence using the FDS.

A candidate shock, or sequence of shocks, could be considered as coverage if it:

• Envelopes the required SRS over the component’s important modal frequency range.
• Produces an FDS equal to or greater than that of the omitted high-frequency random environment over the same frequency range.
• Produces representative stresses and failure modes in the component.
• Does not create excessive low-frequency response or unrealistic interface loading.

Several repeated shocks may be needed to obtain the required fatigue damage. The number, polarity, axis and repetition rate should be selected based on the measured exposure duration and the expected fatigue mechanism. This does not establish universal equivalence between random vibration and shock, but it can provide a defensible component-specific verification method, particularly if supported by a correlated finite element model or by measured transfer functions showing that the shock test excites the same critical modes and produces stress at the same locations as the full-band engine environment.

The shock facility must itself be capable of producing and measuring the required high-frequency content. Depending on the required SRS, a mechanical impact machine, resonant plate, tuned resonant fixture or pyroshock simulator may be more suitable than a conventional electrodynamic shaker.

7. Possible False High-Frequency Responses

Even with good preliminary screening, the following items are worth checking. They are the ones that most often produce convincing but spurious high-frequency peaks.

• Actual mounted accelerometer response. Confirm the calibrated flat-response limit, not merely the accelerometer resonant frequency. Stud mounting on a flat, clean surface generally gives the best high-frequency response. Adhesive pads, brackets, clips and imperfect mounting surfaces can introduce local resonances or filtering.
• Analog anti-alias filtering. Confirm that an analog low-pass filter is applied before digitization. A digital filter applied afterward cannot remove energy that has already aliased into the recorded band. The sample rate should also provide reasonable margin above the highest frequency of interest.
• Sensor and conditioner overload. High-frequency mechanical input can excite the accelerometer’s internal sensing element resonance and momentarily saturate an IEPE amplifier. Once the measurement chain becomes nonlinear it can generate spurious content throughout the spectrum. Check the raw time histories, sensor bias voltage, input range utilization, clipping indicators, and conditioner current and compliance limits.
• Cable motion and connector effects. Clamp the cable close to the accelerometer and inspect for cable whip, triboelectric noise, intermittent connectors and strain at the sensor connector.
• Base strain and transverse sensitivity. A high local strain gradient at the mounting surface can produce apparent acceleration. Comparing different sensor sizes or mounting locations may help.
• Channel crosstalk and grounding. Swap sensors, cables and DAQ channels. Verify whether the peak follows the physical location, the sensor, the cable or the acquisition channel.
• Independent measurement. Place two nearby accelerometers of different models, preferably on different channels or different DAQ units. A laser Doppler vibrometer provides a valuable independent check where access permits.
• Cross-spectral behavior. Compare coherence and phase among nearby accelerometers and, if available, dynamic pressure or microphone measurements. A genuine acoustic mode response should show repeatable spatial and frequency relationships. EMI instead tends to track wiring, grounding or engine electrical events.

One further discriminator is worth adding. Peaks that migrate during a burn are consistent with duct or plume acoustic modes, but they are equally consistent with turbopump shaft orders and blade-passing frequencies, which also sweep with power level. The two scale differently: a pump order remains at a fixed multiple of shaft speed, while an acoustic mode follows the speed of sound and geometry and is sensitive to gas temperature and composition rather than to RPM. Overlay pump speed telemetry on the spectrogram and check whether the ridges hold constant order. The distinction matters, because a stationary tonal pump order is a narrowband-random-on-random problem, while a broadband acoustic mode belongs in the PSD.

Recommended Verification Program

Preserve the full-band data as the actual environmental definition. Use VRS, SRS, FDS and stress-velocity screening, together with component dynamic response information, to determine what portion can credibly be covered by the 2000 Hz shaker test. The resulting program might consist of:

1. A design trade on isolation, evaluated before the test program is fixed. If wire rope mounts can be accommodated, the qualification environment becomes the isolated response and much of what follows may become unnecessary.
2. A conventional 20 to 2000 Hz random vibration test for the lower-frequency environment, derived from the isolated spectrum if isolators are used.
3. A supplemental shock test whose SRS and FDS cover the omitted high-frequency response, where that omitted response is shown to matter.
4. An acoustic test where direct pressure loading is significant. Note that isolation does not help here.
5. Qualification of the isolators themselves over the full temperature range and the full-band unattenuated input.
6. Analysis, heritage, or instrumented engine testing to close any remaining gaps.

And do the stress-velocity screening first. It costs an afternoon and it frequently shows that items 3 and 4 need to address only a narrow set of specific parts, rather than the component as a whole.

References and Further Reading

• F. V. Hunt, Stress and Strain Limits on the Attainable Velocity in Mechanical Vibration, Journal of the Acoustical Society of America, Vol. 32, No. 9, 1960.
• H. Gaberson and R. Eshleman, Modal Velocity as a Criterion of Shock Severity, Shock and Vibration Bulletin 46, 1976.
• T. Irvine, Shock and Vibration Stress as a Function of Velocity, Vibrationdata.
• T. Irvine, Vibration Response Spectrum, Shock Response Spectrum and Fatigue Damage Spectrum tutorials, Vibrationdata.
• S. McNeill, Implementing the Fatigue Damage Spectrum and Fatigue Damage Equivalent Vibration Testing, 79th Shock and Vibration Symposium, 2008.
• D. Steinberg, Vibration Analysis for Electronic Equipment, Wiley.
• C. Harris and A. Piersol, editors, Harris’ Shock and Vibration Handbook, McGraw-Hill, chapters on the theory and application of vibration isolation.
• E. Rivin, Passive Vibration Isolation, ASME Press, 2003.
• L. Demetriades, M. Constantinou and A. Reinhorn, Study of Wire Rope Systems for Seismic Protection of Equipment in Buildings, Engineering Structures, Vol. 15, No. 5, 1993.
• T. Irvine, Vibration Isolation and Miles Equation tutorials, Vibrationdata.
• SMC-S-016, Test Requirements for Launch, Upper-Stage and Space Vehicles.
• NASA-HDBK-7005, Dynamic Environmental Criteria.
• NASA-STD-7001, Payload Vibroacoustic Test Criteria.
• NASA SP-8072, Acoustic Loads Generated by the Propulsion System.

My free ebooks, including the volumes on shock and vibration response spectra and on the stress-velocity relationship, are available at:
https://blog.vibrationdata.com/2025/11/27/toms-ebooks/

If you are working a problem like this one, a plot showing the narrowband PSDs, the maxi-max envelope, the spectrogram, the sensor models, sample rate and anti-alias settings, and the estimated component modal range makes the remaining issues far easier to assess. I am always glad to look.