Correcting Acceleration, Velocity & Displacement Time Histories

There is a need in certain analysis problems to correct an acceleration signal so that its integrated velocity and double integrated displacement each oscillates about its respective zero baseline.  This may require using high pass filtering, trend removal and tapering throughout the integration process.  Trial-and-error is required to select the optimum combination of steps.

The steps are needed in part because the initial velocity and displacement are undefined.  Also, the acceleration may have a spurious offset or trend for the case of measured data.

Furthermore, the resulting displacement should be such that it can be recovered if its then double integrated to acceleration and the acceleration is then double differentiated back to displacement.  This requirement is for rigor.  It yields a consistent set of acceleration, velocity and displacement time histories where each oscillates about its respective zero baseline.

This feature is now included in:

Matlab script: Vibrationdata Signal Analysis Package

Time History > Integrate or Differentiate > Correct Acceleration, Velocity, Displacement

– Tom Irvine

Boeing 717-200


I recently flew as a passenger on a Boeing 717-200 aircraft similar to the one shown in the image.  This aircraft has two Rolls-Royce BR700 engines, with the following specifications:

Maximum Engine Rotational Speeds (Both Engines)

N1 Low Pressure Turbine = 6,195 RPM (103 Hz)
N2 High Pressure Turbine = 15,898 RPM (265 Hz)

I made an audio recording from inside the cabin during take-off and climb-out.


The sound file Fourier transform for a 10-second segment is shown in the image.

The first peak is at 88 Hz, which is 85% of the maximum N1 speed.

The second peak is at 129 Hz and is unidentified.

Most of the higher frequency peaks are integer multiples of 88 Hz.

Complete audio file:  Boeing_717_200.mp3

The Fourier transform was taken from 40 to 50 seconds into the recording.

A “buzz saw” sound occurs due to shock waves at the turbofan blade tips which have a supersonic tangential velocity.

– Tom Irvine

Digitizing Plots


Here is audio/visual file:  Digitizing Plots Here are slides, Matlab scripts and data samples: Here is another script:  digitize_plots.m This is vintage presentation.  I need to add the Matlab scripts to the Vibrationdata GUI package. – Tom Irvine

Notes on Fatigue for Pure Compression Stress

Fatigue is usually associated with tensile stresses.

Engineering knowledge of compressive fatigue is very limited. Compression stresses do not cause cracks, but plastic compressive strain can cause tension stresses when the load is returned to zero and the resulting tension stress causes cracks.

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R = min stress/max stress

But R ->   – infinity   for pure compression stress and with max stress->0

MIL-HBBK-5J S/N curves are typically given for a family of R values starting at a lower limit of R=-1.

So MIL-HBBK-5J is not useful for pure compression.

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Compressive residual stresses can be introduced in the surface by shot peening to increase fatigue life.

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More later…


– Tom Irvine

Webinar 48 – Rainflow Cycle Counting for Multiaxial Stress

Slides: To be added before 4/4/2015

This unit gives a method for converting a time-varying stress tensor into a weighted-average equivalent uniaxial stress. The weights are chosen to maximize the fatigue damage.

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Matlab script: Vibrationdata Signal Analysis Package

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Reference Paper:  Tools for Multiaxial Fatigue

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– Tom Irvine

Webinar 47 – Shock Response Spectrum Synthesis, Special Topics

Slides & Video:


A high-range Cummins Generator in a Seismic Shaker Test.mp4


1. Shaker Table Seismic Testing of Equipment using Historical Strong Motion Data Scaled to Satisfy a Shock Response Spectrum

2. Temporal Moments

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Matlab script: Vibrationdata Signal Analysis Package

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Reference Papers:


From SRS to Temporal Moments

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– Tom Irvine

Fixed-Fixed-Fixed-Fixed Plate, Fundamental Vibration Mode


The plate is aluminum, 0.063 inch thick.  The fixed edge lengths are 6 and 4 inches.

The vibration mode was calculated via the Rayleigh method using an assumed displacement function, as carried out via Matlab script:

The method is given in:  fixed_fixed_fixed_fixed_plate.pdf

See also: Vibrationdata Rectangular Plates

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See also:

Natural Frequencies of a Flat, Rectangular Plate, Finite Element Method

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– Tom Irvine

Webinar 45 – Two-degree-of-freedom System with Rotation and Translation

Slides: webinar_45_two_dof_trans_rot.pptx

Audio/Visual File:

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Matlab script: Vibrationdata Signal Analysis Package

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Reference Papers

Sample Automobile Vibration Problem: auto.pdf

Spring-Mass System Subjected to Enforced Motion: two_dof_enforced_motion.pdf

See also: Dynamic Response to Enforced Motion

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Please send me an Email if you would like to be on the distribution list for the webinar login information.

Tom Irvine