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

Hospital Vibration Environments for Medical Devices



An engineer recently asked me to recommended a vibration test level for his device, which would typically be mounted on a hospital table, including surgical tables.

Well…  shock would almost certainly be worse than vibration, particularly if the device were somehow accidentally dropped on the floor.  Then there are transportation and shipping shock and vibration environments.

A logical approach would be to take some accelerometer measurements on hospital tables, but this is rather impractical for a number of reasons.  One is that there could be wide variation from one hospital to the next, depending on HVAC systems, vibration-inducing surgical devices, etc.

But my acquaintance insisted that he needed a vibration test level for hospital environments.  Well there are no ISO-type standards that specify hospital vibration that I am aware of.  So I made an innovation as shown in the following edited response.

* * *

I am enclosing a paper, which has levels in terms of one-third octave velocity spectra. These are intended as “not to exceed” levels for floor vibration, for both equipment and people.

So here is what I propose for hospitals… Start with the Workshop level in Figure 1 of the paper. This is the highest curve in the family of curves shown.

Assume that the Hospital level would be the same Workshop level, which is conservative for our approach. Now the device may be mounted on a table which amplifies the floor vibration at least at certain frequencies. So add a conservative 12 dB margin as a goal.

The coordinates are shown in the following table.

Freq (Hz) Nominal
Accel (G^2/Hz)
Nominal +12 dB
Accel (G^2/Hz)
4 2e-05 3.2e-04
8 1e-05 1.6e-04
80 1e-04 1.6e-03

The nominal PSD is 0.0634 GRMS overall.

The nominal plus 12 dB is 0.25 GRMS overall.

Power and monitor the device during the following test steps.

Start the test at the nominal level (after the shaker equalization) for some TBD length of time.

Then increase the level in 3 dB increments will the same dwell time as the nominal level.

The goal is the plus 12 dB level.

If the component passes the plus 12 dB, then you are successfully done. If the component fails at a lower level, then we might need to “sharpen the pencil” on the input level, or make design modifications.

The innovation is that we are using a widely-accepted, “not to exceed,” floor vibration level as a basis for deriving a component test level.

* * *

Tom Irvine

Inertial Navigation System Vibration


Ring Laser Gyros


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

* * *

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.

* * *

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.

* * *

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

Jet Aircraft EPNL


There are several tools for analyzing jet aircraft sound as measured on the ground.    The measurements would typically be made for takeoff and final approach at or near an airport.  Fly-over sound levels can also be recorded.

The tools begin with the unweighted, one-third octave sound pressure level (SPL).  One SPL should be taken for each 0.5 second increment.  Furthermore, each SPL should have an overall sound pressure level that is within 10 dB of the maximum overall level.

The tools build upon one another in this order:

  1.  Sound Pressure Level (SPL)
  2.  Perceived Noisiness (Noys)
  3.  Perceived Noise Level (PNL)
  4.  Tone Corrected Perceived Noise Level (PNLT)
  5.  Effective Perceived Noise Level (EPNL)

Each of the functions is in units of dB except for Noys. The Effective Perceived Noise Level is sometimes represented as EPNdB to emphasize that it is a decibel scale.   The functions are defined in Annex 16 of the ICAO International Convention on Civil Aviation, and in the US Federal Air Regulations Part 36.

Noy is a subjective unit of noisiness. A sound of 2 noys is twice as noisy as a sound of 1 noy and half as noisy as a sound of 4 noys.

The Matlab scripts for the EPNL processing are included in the GUI package at: Vibrationdata Matlab Signal Analysis Package

The function can accessed via:

>> vibrationdata > Select Input Data Domain > Sound Pressure Level

An alternative is to compute the A-weighted SPL.  This option is also available in the Matlab GUI package.  Nevertheless, the EPNL is used by convention for jet aircraft noise.

– Tom Irvine