Vibrationdata Matlab Signal Analysis & Structural Dynamics Package


Please send me an Email if you are going to use this package.

Thank you,
Tom Irvine

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Here is a Matlab GUI multi-function signal analysis package:
Vibrationdata Signal Analysis Package

The main script is: vibrationdata.m

The remaining scripts are supporting functions.

This is a work-in-progress. Some features are not yet installed but will be in a future revision. Please check back for updates.

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Currently installed features include:

autocorrelation & cross-correlation
Bessel, Butterworth & mean filters
Fourier transform, FFT, waterfall FFT, spectrogram
FFT for Machine Vibration ISO 10816
PSD, cross power spectral density & energy spectral density
PSD time history synthesis
SRS & SRS Tripartite
SRS time history synthesis
SDOF response to base input and applied force
cepstrum & auto-cepstrum
integration & differentiation
trend removal
rainflow cycle counting
fatigue damage spectrum
ISO Generic Vibration Criteria
modal frequency response functions including H1, H2 & coherence
half-power bandwidth method for damping estimation
generate sine, white noise and other time history waveforms
Helmholtz resonator
spring surge natural frequencies
Davenport-King wind spectrum
Dryden & von Karman gust spectra
Pierson-Moskowitz Ocean wave spectrum
rectangular plate analysis using both classical and finite element methods
spherical bearing stress
unit conversion

Future revisions will have additional functions.

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Please contact me if you have suggestions for added features or if you find bugs.

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See also: Python Signal Analysis Package

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Tom Irvine

Compression after Impact Testing of Composite Laminates Specimens

Figure 1.  Boeing 787 Aircraft

Carbon fiber/epoxy laminates are widely used in aeronautic and aerospace structural components mainly because of their excellent specific mechanical properties.  These laminates show mechanical properties similar or higher than the conventional metallic materials in terms of strength-to-weight and stiffness-to-weight ratios.  The laminates also have higher corrosion resistance.

But the composite laminates may suffer damage during their manufacture, assembly, maintenance or service life, caused by different types of impact, of which low-energy impact is considered the most dangerous because it may not be apparent in a routine visual inspection of the impacted surface.

The impact could result from something as simple as a technician dropping a tool on the laminate surface or from flying debris.

Delamination within composite components is probably the most serious problem, given the difficulty of its visual detection and the extent to which it lowers the mechanical properties. The greatest reduction is that of the compression strength which may be reduced by 60% relative to an undamaged component’s strength.

So damage tolerance is an important factor in the design of aeronautic and aerospace components made of laminated materials. Damage tolerance in laminates is usually studied by determining the effect of different impact energies on their residual strength. The compression after impact (CAI) test is used to test components damaged by low energy impact.

There is a two-step test for assessing potential damage to laminates using small specimen plates.  The first step is do induce damage using an impact.  This is followed by a compression test of the damaged specimen.


Figure 2.  Specimen Mounted in Fixture prior to Drop Weight Impact Damage


Figure 3.   Zwick/Roell HIT230F Drop Weight Tester – Pre-damaging Fiber Composites for CAI Tests

Most of the tests to generate laminate damage are done with a drop weight tower testing device that reproduces the impact of a large mass at relatively low velocity (a few meters per second).  The test machine in Figure 3 can apply impacts with energy levels up to 230 Joules (170 foot-pounds force).

The size of the specimen and the clamping system vary from one study to another but the devices and the procedures are similar.


Figure 4.  Specimen Compression Test

The CAI test measures the residual strength of a composite laminate after being damaged by impact.  The CAI fixture has adjustable side plates to accommodate for both variations in thickness and overall dimension.  The fixture was originally designed by Boeing and outlined in specification BSS 7260.   The fixture with the specimen is tested in either an electromechanical or servohydraulic test machine.  The compression load is increased until the specimen fails.  The typical failure mode is progressive delamination between plies with local buckling.

The CAI fixture frame is designed so that the specimen does not undergo global buckling. The frames vary according to the standard:

  • ASTMBoeingSACMA and DIN: All four sides are guided, but not gripped.
  • ISO, EN and Airbus standards: The upper and lower ends of the specimen are gripped. The sides are guided with linear contact.

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Reference:   Compression after Impact of Thin Composite Laminates

ASTM D7136 / D7136M – 15
Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer Matrix Composite to a Drop-Weight Impact Event

ASTM D7137 / D7137M – 12
Standard Test Method for Compressive Residual Strength Properties of Damaged Polymer Matrix Composite Plates

Boeing, Advanced composite compression test. Boeing Specification Support Standard BSS 7260; 1988.

NASA-STD-5019A, NASA Technical Specification: Fracture Control Requirements for Spaceflight Hardware

Nettles, Damage Tolerance of Composite Laminates from an Empirical Perspective

DOT/FAA/AR-10/6, Determining the Fatigue Life of Composite Aircraft Structures Using Life and Load-Enhancement Factors

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Composite Material Fatigue Notes

The tensile ultimate strength obtained for woven balanced bidirectional laminated carbon/epoxy composites is significantly higher (about 69%) than the compressive ultimate strength. Under tensile loading the composites exhibit brittle behavior, while in compressive tests some nonlinear behavior was observed, which may be consequence of progressive fiber buckling.

P.N.B. Reis, J.A.M. Ferreira, J.D.M. Costa, M.O.W. Richardson, Fatigue life evaluation for carbon/epoxy laminate composites under constant and variable block loading, Composites Science and Technology 69 (2009) 154–160    Link

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The stress ratio   R = (min stress)/(max stress)

Rosenfeld and Huang conducted a fatigue study with different stress ratios to determine the failure mechanisms under compression of graphite/epoxy laminates and showed that Miner’s rule fails to predict composite fatigue under spectrum loading.

Rosenfeld, M.S. and Huang, S.L., “Fatigue Characteristics of Graphite/Epoxy Laminates Under Compression Loading,” Journal of Aircraft, Vol. 15, No. 5, 1978, pp. 264-268.

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A study conducted by Agarwal and James on the effects of stress levels on fatigue of composites confirmed that the stress ratio had a strong influence on the fatigue life of composites. Further, they showed that microscopic matrix cracks are observed prior to gross failure of composites under both static and cyclic loading.

Agarwal, B.D. and James, W.D., “Prediction of Low-Cycle Fatigue Behavior of GFRP: An Experimental Approach,” Journal of Materials Science, Vol. 10, No. 2, 1975, pp. 193-199.

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Fatigue Failure in Fiber Reinforced Laminate Composites

  • matrix cracking
  • fiber fracture
  • fiber/matrix debonding
  • ply cracking
  • delamination
  • combined effects

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– Tom Irvine

Turbine Engine Blade-off Test

Rolls Royce Engine Blade-off Test     Video Link 1     Video Link 2

The engine blade-off test is performed to make sure that the engine can survive a fan. compressor or turbine blade breaking off within the engine, without fragments being ejected through the outside enclosure of the engine.  This is a containment requirement.

A fan blade is deliberately detached during the test using an explosive device while the engine is running at maximum thrust. The test does not require that the engine continues to operate after the blade failure.

The resulting blade loss causes a rotating imbalance force which can induce moderate to severe structural vibration.

For an actual flight occurrence, the engine would be shut down. There is no means of stopping the engine from continuing to rotate while there is sufficient airflow through the fan section to drive the engine. So it would continue to “windmill” without producing any thrust. The rotating imbalance vibration would persist under these conditions.

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Here is a related video on the topic of fan blade loss…

Dr. David Ewins presentation excerpt

See: Exciting Vibrations: The Role of Testing in an Era of Supercomputers and Uncertainties

Go to 27:00 minute mark and watch for about six minutes

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Fatigue accounts for a significant number of turbine and compressor blade failures and is promoted by repeated application of fluctuating stresses. Stress levels are typically much lower than the tensile stress of the material. Common causes of vibration in compressor blades include stator passing frequency wakes, rotating stall, surge, choke, inlet distortion, and blade flutter. In the turbine section, airfoils have to function not only in a severe vibratory environment, but also under hostile conditions of high temperature, corrosion, creep, and thermomechanical fatigue.   Reference

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Flight Case Histories

AirAsia X Flight D7237, Airbus 330, Royce-Rolls Engines June 25, 2017
Video Link 1     Video Link 2

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Southwest B737 near Pensacola on Aug 27th 2016, Uncontained Engine Failure
Report Link

Engine damage seen on the ground (Photo: Peter Lemme)

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Thomas Cook Airline, Airbus A330, Rolls Royce Engines, Turbine Blade Fails
Manchester Airport UK, Monday 24 June 2013.   Video Link   Report Link

The blade failure was caused by high cycle fatigue (HCF) crack propagation with crack initiation resulting from ‘Type 2 sulphidation’ corrosion.

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Qantas Boeing 747-400 near Singapore on May 9th 2011, Fatigue Fracture of Blade 24

The fatigue fracture of blade 24 (Photo: ATSB)

Article Link

The engine was removed and sent for further analysis. Disassembly revealed only minor damage to internal components. The root of the fractured blade was removed and sent for laboratory analysis. The analysis revealed the blade had fractured as result of growth of a low stress/high cycle fatigue crack.

– Tom Irvine

Lomb-Scargle Periodogram


The Lomb-Scargle Periodogram is a least-square method which is useful for calculating the Fourier transform of a time history with gaps or an uneven sampling rate.
Reference Paper

This function has been added to the vibrationdata GUI package

Python script & Utility:

– Tom Irvine

Mode Acceleration and Inertia Relief for a Semi-definite Structural Dynamics System


Aircraft and launch vehicles behave as unconstrained systems in flight, with six rigid-body modes. These vehicles may be “trimmed” using aerodynamic control surfaces and thrust vector control to prevent rotation about the vehicle center-of-gravity (CG).

There is a need to calculate the vehicle’s displacement response to wind, gusts, buffeting and other external forces. This process requires separating the rigid-body response from the elastic response. The elastic response is the relative displacement referenced to the CG displacement. The stress and strain can then be calculated from the elastic displacement response. The method is carried out by inertia relief, where rigid-body motion is constrained by applying an inertial acceleration that is opposite to the acceleration resulting from the external forces.

Here is a paper, which is a work-in-progress inertia_relief.pdf

– Tom Irvine

Fatigue Analysis Webinars


This is a work-in-progress…

I am creating a series of webinars with Matlab exercises for fatigue analysis

Matlab script: Vibrationdata Signal Analysis Package

Here are the slides:

Unit 1  Fatigue Introduction

Unit 2  Fracture

Unit 3  Sine Vibration

Unit 4  Random Vibration

Unit 5  Rainflow Cycle Counting, Time Domain

Unit 6  Sine Sweep Vibration

Unit 7   Synthesizing a Time History to Satisfy a PSD Specification

Unit 8  Drop & Classical Shock  & Video Half-Sine SRS Animation

Unit 9  Seismic & Pyrotechnic Shock & Video Delta 4 Shock Events

Unit 10  SRS Synthesis

Unit 11  Vibration Response Spectrum

Unit 12  Rainflow Fatigue, Spectral Methods, Fatigue Damage Spectrum

Unit 13  Modifying Spectral Fatigue Methods for S-N Curves with MIL-HDBK-5J Coefficients

Unit 14a  Enveloping Nonstationary Vibration via Fatigue Damage Spectra

Unit 14b  Enveloping Nonstationary Vibration, Batch Mode for Multiple Inputs

Unit 15  Using Fatigue to Compare Sine and Random Environments

Unit 16  Sine-on-random Conversion to a PSD via Fatigue Damage Spectra

Unit 17  Non-Gaussian Random Fatigue and Peak Response

Unit 18   Acoustic Fatigue

Unit 19  Shock Fatigue

Unit 20  Fatigue Damage including Mean Stress

Unit 21  Electronic Circuit Board Fatigue, Part 1

Unit 22  Electronic Circuit Board Fatigue, Part 2

Unit 23  Time-Level Equivalence

Unit 24  Multiaxis Fatigue, Constant Amplitude Loading

Unit 25  Multiaxis Fatigue, Stress Ratio Methods

Unit 26  Multiaxis Fatigue, Variable Amplitude Loading

Unit 27  Airbus Fatigue Manual

More later…

– Tom Irvine

Waterfall SRS, 1940 El Centro Quake



The top figure is the time history from the El Centro earthquake, North-South horizontal component.  The second is the corresponding Waterfall FFT with 4 second segments and with 50% overlap.

The Waterfall FFT is calculated by first taking the complete response time history for each natural frequency of interest.  Then the time history for each is divided into segments.  Finally, the shock response spectrum (SRS) is taken for each natural frequency and for each segment, by taking the peak positive and peak negative responses.

The Waterfall SRS function is given in:

Matlab script: Vibrationdata Signal Analysis Package

>> vibrationdata > Time History > Shock Response Spectrum, Various > Waterfall FFT

See also:  El Centro Earthquake

– Tom Irvine

Tom’s Video & Animation Files

Another work-in-progress…

Step 1: Download a video file.
Step 2: Play using VLC media player.

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Launch Vehicles

Delta 4 Heavy Launch Vehicle Shock Events

Pegasus Launch Vehicle

Linear Shaped Charge Test

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Chinook Ground Resonance

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Fixed Wing Aircraft

MD80 Tail Failure

Boeing 747 Wind Tunnel

C-5 Tail Wind Tunnel

Twin Commanche

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Automotive & Transportation

Triple Trailer Oscillation

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Shock & Vibration Testing

Generator Seismic Shaker Test

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Fluid Systems

Pool Slosh 1

Pool Slosh 2

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Half-Sine SRS Animation

Tom’s Conference Papers & Slide Index

I am trying to collect all my presentations. This is a work-in-progress…

Thank you,
Tom Irvine

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NAFEMS World Congress 2017

Introduction to Vibration

Spectral Functions

Random Vibration

Vibration Fatigue

Shock 1 & 2


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Aerospace Spacecraft & Launch Vehicle Dynamic Environments Conference

2017, Statistical Energy Analysis Software & Training Materials, Part 2

2016, Statistical Energy Analysis Software & Training Materials

2015, Seismic Analysis and Testing of Launch Vehicles and Equipment using Historical Strong Motion Data Scaled to Satisfy Shock Response Spectra Specifications

2014, Optimized PSD Envelope for Nonstationary Vibration

2013, Extending Steinberg’s Fatigue Analysis of Electronics Equipment to a Full Relative Displacement vs. Cycles Curve

2012,  Keynote, Dynamics Engineering: A Call to Serve  

2012, An Alternate Damage Potential Method for Enveloping Nonstationary Random Vibration

2011, The NASA Engineering & Safety Center (NESC) Shock & Vibration Training Program

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European Space Agency


ESA Pyrotechnic Shock Distance & Joint Attenuation via Wave Propagation Analysis

ESA Shock Analysis of Launch Vehicle Equipment using Historical Accelerometer Records to Satisfy Shock Response Spectra Specifications 

2016, European Conference on Spacecraft Structures Materials and Environmental Testing

Modifying Spectral Fatigue Methods for S-N Curves with MIL-HDBK-5J Coefficients

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Various Vibration & Fatigue Conferences

VAL2015, A review of spectral methods for variable amplitude fatigue prediction and new results

VAL 2015, Using a Random Vibration Test Specification to Cover a Shock Requirement via a Pseudo Velocity Fatigue Damage Spectrum

ICoEV 2015, International Conference on Engineering Vibration, Derivation of Equivalent Power Spectral Density Specifications for Swept Sine-on-Random Environments via Fatigue Damage Spectra

MOVIC & RASD 2016, Multiaxis Fatigue Method for Nonstationary Vibration

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Shock and Vibration Exchange (formerly SAVIAC)

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Institute of Environmental Sciences and Technology (IEST)

IESTECH 2016, Nonstationary Vibration Enveloping Method Comparison

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Earthquake Engineering Conferences

16th WCEE, Seismic Analysis and Testing of Equipment using Historical Strong Motion Data Scaled to Satisfy Shock Response Spectra Specifications

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2003, A Time Domain, Curve-Fitting Method for Accelerometer Data Analysis

2003, Practical Application of the Rayleigh-Ritz Method to Verify Launch Vehicle Bending Modes

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Sine Sweep vs. Random for Pre and Post Testing


Certain equipment must be designed and tested to withstand vibration.  This is common in the automotive, aerospace, military and other industries.    The equipment is typically mounted to a shaker table and then subjected to a base input random or sine sweep vibration test.   The random vibration is usually in the form of a power spectral density (PSD).

The sine sweep or random test level may represent a maximum expected field environmental, a parts and workmanship screen, or an envelope of both.   The level may also include a statistical uncertainty margin or a safety factor.

A common practice is to perform low-level sine sweep test before and after the full-level test in order to measure the transmissibility ratio and identify natural frequencies and damping ratios.   There must be at least one base input control accelerometer and one reference accelerometer for this test, where the reference accelerometer is mounted somewhere on the test item.   The before and after transmissibility curves are then compared to assess whether any of the response peaks have shifted in frequency or magnitude.   Any shift may indicate that some fasteners have loosened or some other change has occurred.  If so, further investigation is needed.  Ideally, two curves are identical such that no further evaluation is required.

Sine sweep is the traditional vibration test for the pre and post tests.  The purpose of this paper is to determine whether random vibration can be substituted for sine sweep, via an example.  This could be done for time saving.  Also, random vibration is easier to control than sine sweep.

A difference between sine sweep and random is that all modes are excited all the time for stationary broadband random.  There is only one excitation frequency at a given time in sine sweep vibration, and each mode will be excited individually if the modal frequencies are well-separated.  In addition, the random vibration used for shaker testing typically has a bell-shaped histogram curve, whereas sine sweep vibration with constant amplitude has a bathtub-shaped histogram.

Both sine sweep and random should give the same transmissibility results for a linear system per textbook theory, but there are some practical concerns for implementation of each.  The numerical example results will show that random vibration is adequate, although sine sweep remains the best choice because it can give finer resolution.

An example is given in:  sine_sweep_random_pre&post_test.pdf

See also:

Webinar Unit 3 Sine Sweep Vibration 

Beam Bending Natural Frequencies & Mode Shapes

– Tom Irvine