Vibrationdata Matlab Signal Analysis & Structural Dynamics Package


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

Thank you,
Tom Irvine

* * *

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.

* * *

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.

* * *

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

* * *

See also: Python Signal Analysis Package

* * *

Tom Irvine

An Indirect Method for Converting a Shock Response Spectrum Specification to a New Q Value

  •  Aerospace pyrotechnic shock response spectrum (SRS) specifications are almost always given with an amplification factor Q=10
  • Corresponding time history waveforms for the base input acceleration are almost never given with the specifications
  • Users are allowed to synthesize their own waveforms to satisfy the SRS for analysis & test purposes
  • Some shock analysis methods use the SRS directly without time history synthesis, such as modal combination methods
  • The following method enables an SRS specification to be converted to a new Q value for engineering purposes

Slides:  150_SRS_specification_new_Q.pptx

Software: Matlab Vibrationdata GUI

– Tom Irvine

Nastran Modal Transient & Response Spectrum Analysis for Base Excitation


  • Shock and vibration analysis can be performed either in the frequency or time domain
  • The time domain method requires more computation time but is much better suited for transient and nonstationary excitation
  • Time domain methods are also better for rainflow fatigue cycle counting
  • Students should already have some familiarity with Femap & Nastran
  • They should also be able to perform SRS time history synthesis as shown in previous Vibrationdata units
  • NX Nastran is used as the solver, but the methods should work with other versions
  • Two units for direct shock response spectrum analysis is also included

* * * * * * *

Prerequisite Materials

Webinar Index

Structural Dynamics Webinars

Matlab Vibrationdata GUI

* * * * * * *

Main Presentations:

Nastran Modal Transient Slides:  200_FEA_modal_transient_revG.pptx

Nastran FEA Base Excitation via Response Spectrum:  201_FEA_response_spectrum_revE.pptx

Nastran FEA Base Excitation with Multiple Response Spectrum Inputs:  202_FEA_response_spectrum_multiple_revA.pptx

* * * * * * *

Nastran Files

Students should generate their own files, but here are several for reference:





* * * * * * *

See also:    Vibrationdata Nastran

– Tom Irvine

Extract Mass & Stiffness Matrices from Nastran model

The punch file method may be used to extract the mass & stiffness matrices from Nastran models.  The format is awkward since zero terms are not stored.  Also the matrices are assumed to be symmetric, and the upper triangular portion above the diagonal is not stored.

Here is a paper from the Middle East Technical University which explains the format:  paper link.

The key is to apply the following command in the *.nas, *.dat, *.bdf or equivalent file:


Here is a sample file for a fixed-free beam, aluminum, 24 inch long, solid cylinder, 0.25 inch diameter, 24 elements:  beam_24e_diam_0p25_punch-000.nas

Its punch file output is:  beam_24e_diam_0p25_punch-000.pch

The fundamental frequency is 11.9 Hz.

If Femap is used, select the punch output with coupled mass.

Here is a C++ program which converts the punch file into full mass & stiffness matrices in ASCII text format:



The mass & stiffness matrices can then be imported to Excel, Matlab or some other program.

– Tom Irvine

Cuba Sonic Attack Analysis


A sound file from the attack on the U.S. Embassy in Cuba has now been made available on the Internet.  I did a spectral analysis of this file using my Matlab GUI scripts.  The sound source is still unknown.  The attacks have caused hearing, cognitive, visual, balance, sleep and other problems for embassy personnel.

Here is a quick look paper: Cuba_sonic_analysis.pdf

Here is the sound file: Cuba_sonic.mp3   Turn up the speaker volume to hear the sound.

– Tom Irvine

NASA SP-8072 Launch Vehicle Liftoff Acoustics


NASA SP-8072  Acoustics Loads Generate by the Propulsion System

The liftoff analysis has been added to the GUI package at:  Vibrationdata Matlab GUI

The function can be accessed via:

>> vibrationdata > Miscellaneous Functions I > Acoustics Vibroacoustics & SEA > acoustics > Launch Vehicle Liftoff Acoustics

Here is document which gives further details using an older C++ version: liftoff_notes.pdf

* * * * *

The aerodynamic flow-induced pressure during the transonic and maximum dynamic pressure phases can be calculated using the follow tools:

Prediction of Sound Pressure Levels on Rocket Vehicles During Ascent: flow.pdf

This function can be accessed via:

>> vibrationdata > Miscellaneous Functions I > Acoustics Vibroacoustics & SEA > acoustics > Launch Vehicle Aerodynamic Flow

– 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.

* * * * *

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

* * * * *

Composite Material Fatigue Notes


Examples of failures following fatigue testing: (a) positive stress ratio (R = 0.05) and (b) negative stress ratio (R = -0.5).

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

* * * * *

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.

* * * * *

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.

* * * * *


Fatigue Failure in Fiber Reinforced Laminate Composites

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

* * * * *

– 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.

* * * * *

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

* * * * *

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

* * * * *

Flight Case Histories

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

* * * * *

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

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

* * * * *

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.

* * * * *

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

See also:  The Mode Acceleration Method  MA_method.pdf

– Tom Irvine