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

– 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

Huntsville University Drive Bridge Vibration


This bridge, near the University of Alabama in Huntsville, was built so that pedestrians and cyclists could safety cross over the road. The support structures on either end have both stairs and gentle ramps.

The bridge’s fundamental frequency is 2.2 Hz with 0.16% damping. The damping is very low. These values were determined via experiment in  Bridge vibration report.

The triaxial accelerometer & data logger was a Slam Stick provided by Mide.

The Matlab scripts for the accelerometer data post-processing are included in the GUI package at: Vibrationdata Matlab Signal Analysis Package

See also: London Millennium Bridge Vibration

* * * *

Here is another Huntsville-themed paper: Huntsville Hospital Tram Vibration

– Tom Irvine

Shock and Vibration Severity Thresholds for Structures and Equipment

Launch vehicle and spacecraft equipment must withstand pyrotechnic shock from stage separation and other flight events.   Civil engineering structures and equipment must survive seismic events.  There are many other examples where military, automotive, telecommunication and other equipment must be designed and tested to meet shock requirements derived from field or flight data.  The likelihood that a structure or equipment piece will fail a shock environment is often expressed in terms of a severity threshold.  The threshold may be expressed in terms of a base input or response level.  The purpose of this paper is to compile severity acceleration and velocity thresholds for both equipment and buildings into a single document for comparison purposes.

Link:  shock_vibration_severity_thresholds.pdf

* * *

See also:
Shock Severity Limits for Electronic Components
Dr. Howard Gaberson’s Papers
Stess-Velocity Relationship

– Tom Irvine

Hypersphere SRS


Figure 1. El Centro Earthquake 1940, Peak Pseudo Velocity, 36.4 in/sec
Launch vehicle and spacecraft equipment must withstand pyrotechnic shock from stage separation and other flight events. Civil engineering structures and equipment must survive seismic events. There are many other examples where military, automotive, telecommunication and other equipment must be designed and tested to meet shock requirements derived from field or flight data. The specification is commonly given as a shock response spectrum (SRS). An SRS may be calculated for each orthogonal input axis, assuming the availability of triaxial accelerometer data. Each axis may thus have a separate specification. Alternatively, a maximum envelope can be drawn over the three SRS curves and then applied as a uniform specification to each orthogonal axis.

The uniform enveloping method, however, can underestimate the maximum resultant shock when all possible orthogonal axes sets are considered. The purpose of this paper is to introduce a hypersphere method to achieve a true maximum SRS.

Paper link:  hypersphere_SRS

The Matlab script for this calculation is included in the GUI package at:
Vibrationdata Matlab Signal Analysis Package

– Tom Irvine