Some Nonlinear Sine Sweep Vibration Test Data

Certain equipment must be designed and tested to withstand external vibration excitation.  This is common in the military, naval, aerospace and other industries.

The equipment is typically mounted on a shaker table and subjected to base excitation.  The input may be random vibration if the field environment is likewise.  In other cases, random vibration is used to verify the integrity of parts and workmanship separately from the maximum expected field environment.

The random vibration is typically specified as a power spectral density (PSD).  Note that the workmanship screen and field level can be enveloped by a single PSD. A goal is to verify that the equipment operates properly before, during and after the random vibration test.

A more thorough test is to perform a sine sweep test before and after the random vibration test.   A response accelerometer is mounted on the test article, in addition to the control accelerometer at the base input location.   The objective is to determine whether any natural frequencies have shifted, or any other changes have occurred, as a result of the random test.  Such changes could indicated loosened fasteners, crack formation or other defects.

A case history is given next.  The data was sent to me by a colleague.  I have requested further information on the equipment and will post a photo or diagram later if permission is granted.


Figure 1.

Figure 2.

A rocket engine assembly was subjected to a sine sweep test in conjunction with a random test.  A resonant response occurred when the excitation frequency was swept through 85 to 86 Hz as shown in Figure 1.  The equipment response would have had a similar frequency content to the input if it had been a well-behaved, linear, single-degree-of-freedom system.  The response Fourier transform for the corresponding duration did have a spectral peak at 85.45 Hz matching the sweeping input frequency as shown in Figure 2.

(Note that this is an approximation because the Fourier transform is taken over a short duration and represents an average, whereas the input frequency has instantaneous change.)

But the response also showed integer harmonics with the highest peak at 683.6 Hz, which was 8x the fundamental frequency.

Please let me know if you have observed similar effects or have other insights.  Hopefully, I can post more details later…

Sine Sweep Time History Data

Thank you,
Tom Irvine

* * *

My colleague Albert Turk sent me a reply, paraphrased as follows:

I suspect a component with a resonance at the input frequency that is excited to the point of metal-to-metal impact. I have seen data from repetitive impact machines (HASS) and also from gunfire (50 cps) that had these integer multiples.

If so, the sinusoidal excitation has turned the assembly into a repetitive impact machine near 85 Hz. It would be interesting to see if there is a sine input amplitude threshold below which this suddenly goes away.

And Steve Zeise wrote:

I have observed this phenomenon and tracked it down to loose joints introducing impacts into the system.

Note that joints can slip under shock & vibration loads.

“Loss of clearance” of “loss of sway space” may be appropriate, related terms to describe the problem shown in the data.  Further investigation is needed.

LDS V-8900 Shaker Table


Years ago, I had the opportunity to perform hands-on shaker table testing, mostly for avionics components.  That was a great learning experience.  Alas, that opportunity has gone, but I am still involved writing software and providing training for test engineers.

LDS was one of the shaker manufacturers during my testing days.  LDS has since merged with Bruel & Kjaer.

I met my colleague Joel Leifer at an engineering conference recently.  He informed me about a new LDS shaker model, which has a 4 inch displacement stroke.  This would be very useful for low frequency shock and vibration tests.  Videos and further information is given at:  Video Link

* * *

Joel wrote:

I am interested in working with the space community as they define test requirements as this could be the tool they have been looking for to do some of the harder tests. Any advice or guidance you could give will be greatly appreciated.

Thanks for your attention to this.


Joel Leifer, PE
District Manager (Western Region) VTS
Bruel & Kjaer North America
8566 Van Ness Ct Unit 24F
Huntington Beach, CA 92646
Direct: 817 475-2329

So please contact Joel if you are interested in collaboration, etc.

I was going to ask Joel to provide a demo model for me so that I could do some science projects at my home, but my wife would never let me keep a shaker table in our garage :)

– Tom Irvine

JPL Tunable Shock Beam




The NASA/JPL Environmental Test Laboratory (ETL) developed and built a tunable beam shock test bench based on a design from Sandia National Laboratory many years ago. ETL has been using this test system successfully since October 2008.

The excitation is provided by a projectile driven by gas pressure.

The beam is used to achieve shock response spectrum (SRS) specifications, typically consisting of a ramp and a plateau in log-log format. The intersection between these two lines is referred to as the “knee frequency.” The beam span can be varied to meet a given knee frequency. The high frequency shock response is controlled by damping material.

The tunable-beam system is calibrated with a center-of-gravity (CG) mass and footprint model of the test article. The mass simulator is mounted in the test axis with the appropriate accelerometers installed as they would be for the testing the test article. Then the system is tuned by performing test runs until the data plots meet the requirement.

Finally, the test article is mounted to the tuned beam for the actual test.

See also:  JPL Tunable Beam

– Tom Irvine

French Passenger Train Vibration


I recently rode in the above French TER, Electric Train, Model Z 24500, Lyon to Annecy.


A sample accelerometer time history is shown above.  The sensor was mounted on a passenger car floor, a Slam Stick X, sampled at 400 samples/sec.


The spectrogram of the accelerometer data shows a cluster of peaks from 1 to 2 Hz.  These are mostly likely due to the interaction between the wheels and the track joint gaps.  The track length and the train speed would need to be identified in order to resolve this.    But here is a rough estimate using assumed values for speed and length:

speed/length = (25 m/sec) / 20 m = 1.25 Hz

Minor speed variations would cause the peaks to have some drift.

Some intermittent peaks also occur near 8 Hz.  Here is another rough calculation.  Assume that the wheels have a 1-meter diameter, with a circumference of pi meters.

speed/circumference = (25 m/sec) / (pi meters) = 8 Hz.

So the peaks near 8 Hz appear to be due to wheel static imbalance.

Also note that the electrical power frequency is 50 Hz, so the engine may have a component at this frequency.

Matlab Data:  French_train.mat

– Tom Irvine

Embraer E190 Landing Shock



I recently flew as a passenger on a E190 similar to the one in the top image. The landing shock is shown in the bottom image. The data was recorded on a Slam Stick X, sampled at 400 samples/sec. The initial set of peaks have a frequency of about 0.9 Hz.

Matlab File: E190_landing_shock.mat

See also: Landing Shock

– Tom Irvine

A330-200 Landing Shock


Image Courtesy of Justin Kane

I recently flew as a passenger on a A330-200 similar to the one in the image.  I used a Slam Stick X Vibration Data Logger to measure the landing shock, with the sensor mounted on the cabin floor.  The acceleration time histories for two axes are shown in the following figures.



The vertical axis response has several spectra between 0.5 and 2.0 Hz.

A330-200 Landing Shock Matlab file

See also:  Landing Shock

– Tom Irvine

Modal Test Problem & Solution

Ideally, a modal test on a structure would be performed with completely free boundary conditions.  This configuration can be approximated by mounting the structure on compliant air cushions, or by suspending it with elastic cords, so that the mounted natural frequency is much smaller that the structure’s fundamental frequency.

Other choices would be to test the structure with one boundary fixed, or in its final installation configuration.

But there may be certain cases where a structure can only be tested at its “next higher level of assembly.”  NASA is facing this issue for a launch vehicle which can only be tested on its launch platform and tower assembly due to cost and schedule reasons.

The modal test results will thus be for the complete system rather than the vehicle by itself.  But the need is for the vehicle’s modal parameters, which can then be used to calibrate the stiffness in a finite element model.  This would be for the case immediately after liftoff when the vehicle boundary conditions are free-free.  The vehicle natural frequencies and mode shapes are needed to check control stability, structural stresses, etc.

Here is paper which offers a potential solution by extracting the subsystem stiffness matrix from system level modal test results with a known mass matrix.  A simple three-degree-of-freedom system is used.  The parameters are conceptual only and do not represent those of the launch vehicle and its platform.

Note the reduction method in this paper may be similar to System Equivalent Reduction Expansion Process (SEREP) which is used in the automotive industry.

See also:

Receptance Decoupling for Two Rigidly Connected Subsystems

Determination of the Fixed-Base Natural Frequencies for a Two-degree-of-freedom System via Modal Test Receptance

– Tom Irvine

A320 Landing Shock


I recently flew as a passenger on a A320 similar to the one in the image.  I used a Slam Stick X Vibration Data Logger to measure the landing shock, with the sensor mounted on the cabin floor.  The resulting acceleration time history is shown in the following two figures, longer and shorter views.  The main wheels touch down at the zero second mark. The nose wheels contact the runway about 3.5 seconds later.



The higher frequency energy between zero and 0.5 seconds consists of components in the 10 to 15 Hz frequency domain, likely representing structural modes.  The sample rate was 400 samples per second.

A320 Landing Shock Matlab file

See also: Landing Shock

– Tom Irvine

SRS Synthesis – New Option


(Click here for better image of Matlab GUI screenshot)

I have added an “Exponential Decay” option to the wavelet synthesis function in the Matlab GUI package.  The goal is to synthesize a wavelet series that has a gradual overall exponential decay, somewhat similar to an actual pyrotechnic or seismic shock event. Here is an example.

The advantage of using wavelets as a basis is that each has zero net velocity and zero net displacement, as does a complete series.  These conditions are needed for both analysis and testing.

Note that some pyrotechnic SRS specifications begin at a natural frequency of 100 Hz. A good practice is to extrapolate the specification down to 10 Hz, especially if there are any vibration modes below 100 Hz.

The Vibrationdata Matlab GUI package is given at: Vibrationdata Matlab Signal Analysis Package

* * *

I previously came up with a method which synthesized a series of damped sines to satisfy an SRS.  The damped sines where then decomposed into a wavelet series.  The previous method is still available.   See Webinar 27 – SRS Synthesis

– Tom Irvine

Matlab Batch Process via Vibrationdata GUI


I have added batch processing as an option for time histories as shown above.  I will add more options in upcoming revisions.  The Vibrationdata Matlab GUI package is given at: Vibrationdata Matlab Signal Analysis Package

Here are some sample input files for practicing batch processing: batch_sample.mat

Tom Irvine