Satellite Equipment Vibration Testing


Stentor Satellite

Equipment mounted in satellites must withstand acoustic-driven random vibration at liftoff and during the transonic and maximum dynamic pressure phases of flight.   The equipment must be designed and test accordingly.

The equipment is mounted on shaker tables for the random vibration testing, but this can be overly conservative with respect to the actual vibroacoustic environment.

Here is an interesting case study paper:

Comparison of Satellite Equipment Responses Induced by Acoustic and Random Vibration Tests, Bertrand Brevart, Alice Pradines, 2002. Comparison_Satellite_2002.pdf

Force-limiting is one method for mitigating this overtest problem.  See NASA-HDBK-7004

More later…

– Tom Irvine

Inertial Navigation System Vibration


Ring Laser Gyros


IMU – inertial measurement unit
INS – inertial navigation system
RLG – ring laser gyro

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An INS uses the output from an IMU, and combines the information on acceleration and rotation with initial information about position, velocity and attitude. It then delivers a navigation solution with every new measurement.

This process, called mechanization, is the summation of acceleration and attitude rate over time to produce position, velocity and attitude.   The mathematics require coordinate transformation and integration.

An IMU is typically composed of the following components:

• Three accelerometers
• Three gyroscopes
• Digital signal processing hardware/software
• Power conditioning
• Communication hardware/software
• An enclosure

Three accelerometers are mounted at right angles to each other, so that acceleration can be measured independently in three axes: X, Y and Z. Three gyroscopes are also at right angles to each other, so the angular rate can be measured around each of the orthogonal axes.

The gyroscopes were traditionally spinning wheel devices.  Nowadays, there are MEMS, fiber optic and ring laser gyros.

Vibration environments can adversely affect the accuracy of the IMU data.   Some of the potential issues are: aliasing, stability, bias drift, saturation, linearity, random walk and latency.

An IMU may be mounted via isolators.  As an example, the Space Integrated GPS/INS (SIGI) Inertial Sensor Assembly is isolated with a natural frequency of 55 Hz and 13.5% damping, equivalent to Q=3.7.

The purpose of the IMU is to measure rigid-body motion.  But the sensors also record the vehicle’s  elastic body vibration.  The control algorithms must be designed accordingly. Also, any isolation method must not be allowed to degrade the IMU accuracy.

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The Nyquist frequency is equal to one-half the sampling rate.

Shannon’s sampling theorem states that a sampled time signal must not contain components at frequencies above the Nyquist frequency. Otherwise, an aliasing error will occur.

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Here are some papers:

Notes on sample rate and aliasing:aliasing_notes.pdf

Inertial Navigation System Dither Sound & Vibration Test: INS_dither.pdf

Sound File:  dither.mp3

– Tom Irvine

Extending Steinberg’s Fatigue Method


Here is a paper for…

Extending Steinberg’s Fatigue Analysis of Electronics Equipment Methodology to a Full Relative Displacement vs. Cycles Curve



This paper also shows in a very roundabout way that “fatigue damage equivalence” between sine and random vibration occurs when the sine amplitude (zero-to-peak) is approximately equal to the random vibration 2-sigma amplitude.

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Here is a Matlab script for cumulative damage index calculation, to be used after rainflow cycle counting:  RD_N.m

This script is for identifying individual points along the RD-N curve:  RD_N_point.m

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See also:

Rainflow Cycle Tutorial Paper

Rainflow Fatigue Cycle Counting

PSD Time History Synthesis

Steinberg’s Vibration Analysis for Electronic Equipment

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– Tom Irvine

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Pyrotechnic Shock Characterization Testing

Pyrotechnic devices such as linear shaped charge and frangible joints are used for stage and fairing separation in launch vehicles. These devices generate high-frequency mechanical shock energy. Avionics components mounted in the vehicle must be designed and tested to withstand this shock energy.

Thus, ground testing is needed to measure the pyrotechnic shock levels so that component test levels can be derived. Measurements are typically taken near the source and at locations away from the source where components are to be mounted.

Ideally, this ground testing is performed using flight-like structures with connected cylindrical modules, fairings, etc. Cost and schedule concerns, however, may drive program managers to perform alternate tests instead, using curved or even flat panels with partial segments of the actual separation device.  In some cases, these subscale tests are used for source shock measurement only.

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Stage separation events have the potential to excite the ring frequency of cylindrical structures as well as other cylindrical modes.

Note that wave propagation in a cylinder is governed by the Donnell-Mushtari-Vlasov eighth-order partial differential equation (or by an equivalent pair of coupled lower-order equations.) This equation covers both bending and membrane effects.

On the other hand, bending waves in rectangular plates are governed by a single, fourth-order equation.

All of this is a fancy way of saying that a cylinder responds to pyrotechnic shock much differently than a rectangular panel does.

Furthermore, cylindrical shells are much more representative of actual flight structures that are separated by pyrotechnic devices than rectangular panels are.

So I recommend testing with full, cylindrical structures.  The structures should also have mass simulators for the avionics components.

An example of a ground test where a ring mode was apparently excited is given at: Ring Vibration Modes.  See Appendix B in this paper.

See also:

Shock Response Spectrum Page

Rings, Cylinders, Shells & Cones Page

– Tom Irvine

The Great Amplitude Format Debate

Shock and vibration test specifications for avionics and military equipment have almost always been specified in terms of acceleration. The main reason is that acceleration can easily be measured by accelerometers.

Velocity sensors are also available but are less common.

Gaberson, Chamblers et al, claim that pseudo velocity bests represents the damage potential of a shock or vibration event.  Pseudo velocity is the relative displacement multiplied by the natural frequency (rad/sec).  This assertion has merit.  I have written a paper on this subject at: sv_velocity.pdf

On the other hand, Steinberg gives empirical formulas for the fatigue potential for both shock and vibration for circuit boards in terms of relative displacement.  The formulas are given in Steinberg’s Book.

The shock response spectrum can be plotted in tripartite format, showing each of the three amplitude metrics as a function of natural frequency.  A good engineering practice is to review all three response parameters in this format for thoroughness.

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There are two pseudo velocity metrics.

Let omega be the natural frequency in (rad/sec)

The pseudo velocity shock spectrum (PVSS) is calculated by multiplying the relative displacement SRS value by omega.

The acceleration pseudo velocity shock spectrum (APVSS) is obtained by dividing each acceleration SRS value by omega.

Dr. Howard Gaberson has generated some examples which show that the PVSS and APVSS are nearly equal except at very low natural frequencies where the APVSS tends to be higher.

In addition, the true relative velocity can be calculated using the method in:  ramp_invariant_base.pdf

The two pseudo velocity metrics and the true relative velocity metric can be used somewhat loosely and interchangeably in regard to damage potential estimation.  Further experiments and research are needed to refine these concepts.

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See also:

Dr. Howard Gaberson’s Papers

SRS Tripartite

Stress-Velocity Relationship

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– Tom Irvine

Enveloping Nonstationary Random Vibration Data

Launch vehicle avionics components must be designed and tested to withstand random vibration environments.  These environments are often derived from flight accelerometer data of previous vehicles.    This data tends to be nonstationary as shown in the figure above.

The typical method for post-processing is to divide the data into short-duration segments.  The segments may overlap.  This is termed piecewise stationary analysis.

A power spectral density (PSD) is then taken for each segment.  The maximum envelope is then taken from the individual PSD curves.

The maximum envelope for a completed mission can be used to check the test levels for components which flew on that mission.

In addition, the maximum expected flight level (MEFL) for a future mission can be derived from the maximum envelope with the addition of an appropriate statistical margin.  The component acceptance and qualification test levels can then be derived from the MEFL.

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A more realistic enveloping method is to use the damage potential based on rainflow cycles, which accounts for fatigue.  This method is described in: Nonstationary Damage Potential.   I developed this method in collaboration with Sam DiMaggio of SpaceX and with Vince Grillo of NASA Kennedy Space Center.

Here is the PowerPoint version.

The software programs for this method, both source code and executable files, are given at:  Vibrationdata Nonstationary Page.   The software is available on a subscription basis.

Tom Irvine

PS: After writing this paper, I learned that Scot McNeill had previously published a similar paper: FDS_FDET_McNeill.pdf. So I may have reinvented the wheel on this one. But I whimsically noticed that Scot used two of my previous papers as references in his own paper.

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See also:

Fatigue Damage Spectrum

Optimized PSD Envelope for Nonstationary Vibration

Avionics Box Isolation

I have written some tutorials on avionics component isolation which may be downloaded at:



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The Matlab GUI scripts are given in the GUI package at:  Vibrationdata Matlab GUI Package

The function is accessed via:

Miscellaneous > Structural Dynamics > Spring-Mass Systems > MDOF > Six-DOF Mass with Four Isolators

The Six-DOF scripts calculate the natural frequencies and mode shapes for a component mounted via four isolators. It also has options for the acceleration response to base input excitation.

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See also:

Damping, Isolation & Vibration Absorbers Page

Vibration Isolation Basics

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Tom Irvine

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