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

Alternate Link for 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.

The download and extraction process should be straightforward, but here are some slides for those who need instruction:  Vibrationdata_download.pptx

See also:  An Introduction to Shock & Vibration Response Spectra eBook

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Here are some webinar and slide presentations which demonstrate the use of the GUI package in exercises:

Webinar Index

Structural Dynamics Webinars

Fatigue Webinars

Seismic Test & Analysis Webinars

Circuit Board Shock & Vibration Analysis

Nastran Modal Transient & Response Spectrum Analysis for Base Excitation

Launch Vehicle Vibroacoustics

Vibroacoustics/Statistical Energy Analysis

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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

Architectural Helmholtz Resonators


Tapiola Lutheran Church in Espoo, Finland, Opened in 1965

Helmholtz-type resonators are built into the walls of the church.  The slots between brick pairs and cavities behind them act as both absorbers and diffusors of sound.  The absorption reduces the reverberation time as desired for speech intelligibility during sermons.  Some reverberation is desirable, however, to enhance organ music.

A Helmholtz resonator is a volume of air which is enclosed in a container with at least one opening. It is also called a cavity resonator.  The air in the container’s neck acts as a mass. The air in the volume acts as a spring. The Helmholtz resonator thus behaves as a mechanical spring-mass system.

Bankstown-court-house-Decor-Trend-ceiling-by-Decor-SystemsCourtroom in Bankstown, NSW, Australia, with slotted panels for reverberation reduction.


Slotted block absorbers in a gymnasium.

BT240 5

The BT240 slotted modular bass trap panel provides excellent absorption down to 65 Hz.

– Tom Irvine

Material Shock Loading



The area under each stress-strain curve represents the maximum energy that can be absorbed and is a measure of toughness.

Ductile materials undergo observable plastic deformation and absorb significant energy before fracture.  Brittle fracture is characterized by very low plastic deformation and low energy absorption prior to breaking.

Toughness is the ability of a material to absorb energy and plastically deform without fracturing. One definition of material toughness is the amount of energy per unit volume that a material can absorb before rupturing. This measure of toughness is different from that used for fracture toughness, which describes load bearing capabilities of materials with flaws.

Toughness requires a balance of strength and ductility. A material should withstand both high stresses and high strains in order to be tough. Generally, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupturing.

Toughness (or, deformation energy, UT) is measured in units of joule per cubic metre (J·m−3) in the SI system and inch-pound-force per cubic inch (in·lbf·in−3) in US customary units.



Stress Strain Test Data Reference

As an example, consider that a plate made from A286 Stainless Steel must withstand shock loading defined by the following acceleration shock response spectrum (SRS) and its corresponding pseudo velocity response spectrum.  Note that A286 is a ductile material with excellent toughness.



The conversion formula is:    PV SRS (f) = scale*[Accel SRS (f) / (2 π f) ]

For English units:  scale = 386 in/sec^2 / G

The natural frequency of the plate is unknown.  So assume the peak pseudo velocity of 250 in/sec, which is the plateau.

The strain-velocity relationship for a plate is:

ε ~ 2 * ( PV / c ) = 2 * PV *sqrt( ρ / E )

c = sqrt ( E / ρ )

PV = pseudo velocity
c = speed of sound in the material
E = elastic modulus
ρ = mass/volume

Note that the elastic modulus is a function of strain, and thus the speed of sound is also.


The velocity-strain graph is difficult to derive given the need to take the slope of the plotted nonlinear stress-strain curve.  The velocity-strain graph is plotted up to 0.2 strain because this is the point at which the elastic modulus becomes approximately zero.

The resulting strain for 250 in/sec is per the graph is  ε = 0.0037, or it could jump to ε = 0.021 depending on the response time history.

Both strain estimates show that the material will yield but is well within its fracture limit per the previous stress-strain curve.    The engineering fracture strain threshold is above 0.2 for A286 stainless steel.  The yield point for engineering material in general is defined as 0.002 strain.

Note that this approach is a rough approximation given that the shock response spectra curves assumed a linear model.  Further research is needed.

Stress Strain Velocity Relationship Paper

Stress Velocity Relationship

– Tom Irvine

Golden Gate Bridge Singing


Golden_Gate_singing2Some San Francisco Bay Area residents from Marin County to the Presidio have noticed a sustained, series of high-pitched tones.  The sound reached a new peak volume, and recordings of the eerie noise spread across social media in early June,.

The sound is due to high northwest winds blowing through the slats of the Golden Gate bridge’s newly-installed sidewalk railing.   The new slats were thinner than the ones in the previous railing.   The purpose of the new design is to make the span more aerodynamically stable on gusty days.

The sound is most likely an Aeolian tone, a noise produced when wind blows over a sharp edge, resulting in tiny harmonic vortices in the air.

The modification of the Golden Gate Bridge railing is the most recent and most audible element of a multi-phase retrofit that has been underway since 1997. Following the magnitude 6.9 Loma Prieta Earthquake in 1989, The Golden Gate Bridge, Highway, & Transportation District began to prepare the iconic bridge for the wind and earthquake loads that it may encounter in the future.  The design maximum wind speed is 100 mph.

A sample sound file of the Bridge’s tones is taken from:

It was converted to mp3 format using an online utility.  Golden_Gate_singing.mp3

The mp3 file was then called into Matlab and processed using the Vibrationdata tools.

Spectral peaks occur at 354, 398, 439 & 481 Hz.  The spacing is nearly uniform with an average separation of 42.3 Hz.   The nearest musical notes are F, G, A & B, respectively.

The maximum individual peak occurs at 439 Hz. Higher frequency peaks occur at 880, 1051 & 1160 Hz.

Note that these frequencies should vary with wind speed per the Strouhal number.  The formation of the “vortex street” also depends on the Reynold’s number.



Vortex shedding behind a circular cylinder. In this animation, the flow on the two sides of the cylinder are shown in different colors, to show that the vortices from the two sides alternate. Courtesy, Cesareo de La Rosa Siqueira.


See also:  Golden Gate Bridge Wind Tunnel Testing

– Tom Irvine

PSD Fatigue Damage Severity Criteria



PV = pseudo velocity

The following method is intended for components which are to be tested to power spectral density (PSD) specifications on shaker tables. The method can be applied to sine-on-random specifications as well.

The purpose of this document is to recommend velocity severity categories for PSD base inputs in terms of Stress-Velocity Relationship (SVR) fatigue damage.

The categories can then be used to plan the design and analysis efforts required to ensure that a component will pass its PSD test, or at least mitigate risk of failure with associated cost and schedule delays.

The method draws from Gaberson, Steinberg, Morse and Dirlik.

Slides:  psd_severity_revA.pptx

Matlab Scripts: Vibrationdata Signal Analysis Package

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See also:

Dr. Howard Gaberson Papers

Shock and Vibration Severity Thresholds for Structures and Equipment

Shock Severity Limits for Electronic Components

– Tom Irvine

Hot Fire Test of an Upper Stage Rocket Engine


Liquid fuel rocket engines undergo hot fire testing before flight in order to verify their performance, design integrity, etc.  The engines are mounted to heavy-duty, immovable stands for this purpose.   These tests are also referred to as static fire tests.

Furthermore, the tests are almost always performed at ground ambient air conditions, which is appropriate for first stage engines.  Similar tests are performed for solid rocket motors.

Upper stage engines are also subjected to ground ambient air static fire tests.  But the test data is skewed by the atmospheric pressure effects.  These engines can and should also be fired in altitude simulation chambers, although these more realistic tests are more expensive and time-consuming than open air tests.  An example is the NASA Glenn In-Space Propulsion Facility.

Rocket engine designs often incorporate high expansion ratio nozzles for increased performance.

The flow in the nozzle will separate from the nozzle wall, with a resultant reduction in thrust when these nozzles are operated in an ambient pressure significantly higher than what they were designed for.

Separated flow can also cause nozzle burning due to the shock wave that exists at the separation point, nozzle damage due to unsymmetrical pressure distribution, and excessive vibration as the separation point moves erratically around the nozzle.

The following paper shows that the rocket engine overall vibration level may be as much as 18 dB higher at ground ambient air versus altitude simulation:   Influence study of flow separation on the nozzle vibration response

– Tom Irvine

Blue Origin Employment Opportunities


New Shepard Launch

I have been working at Blue Origin in Kent, WA since February 2019.  This is an excellent work environment with engaging technical opportunities.

Blue Origin is hiring engineers including some for vibroacoustics.

Please see:

Applicants must be a U.S. citizen or permanent resident (current Green Card holder), or lawfully admitted into the U.S. as a refugee or granted asylum.

You are welcome to apply via the above link.  Please also send your resume to me if you are interested in vibroacoustics.

Thank you,
Tom Irvine

Launch Vehicle Separation Source Shock Scaling Hypothesis

Consider the case where flight or test pyrotechnic source shock data has been measured on a launch vehicle with a 1-meter diameter aluminum cylindrical shell.  Assume that the source device is frangible joint with a certain number of grains per length.  Now the same device will be used on a new 5-meter diameter vehicle with all other variables remaining the same. The question arises as to how the 1-meter data source shock data can be extrapolated to the 5-meter diameter vehicle prior to any testing of the new vehicle’s structure.

A hypothetical method is presented in:  source_shock_hypothesis.pdf

This method maintains a constant pseudo velocity at the knee frequency as the frequency is shifted for the new vehicle.  Note that the knee frequency is the same as the respective ring frequency.

Experimental verification is pending, but the method is rational.

See also: pyrotechnic shock 

– Tom Irvine

More Launch Vehicle Vibroacoustics

This is a work-in-progress.

Here are some slide presentation with an emphasis on launch vehicles.

Equivalent Static Loads for Random Vibration & Alternate Link

Damping & Isolation & Alternate Link

Liftoff Vibroacoustics & Alternate Link

Ascent Vibroacoustics & Alternate Link

Launch Vehicle Pogo, Combustion Instability and Thrust Oscillation & Alternate Link

Launch Vehicle Statistical Energy Analysis & Alternate Link

Modal Testing, Part I & Alternate Link

The Matlab GUI package and additional slide presentations may be downloaded at:

Vibrationdata Matlab Signal Analysis & Structural Dynamics Package

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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 & Alternate Link

See also:

NASA SP-8072 Launch Vehicle Liftoff Acoustics 

Vibroacoustics/Statistical Energy Analysis

Non-Gaussian Acoustic Pressure Amplitudes in High-Intensity Sound Fields

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Launch Vehicle Tip Over Analysis

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– Tom Irvine

State-Space Method for Systems with Dashpot Damping


Structural dynamics systems can be represented in terms of mass, damping and stiffness matrices.  Each of these matrices may be coupled depending on the model complexity, degrees-of-freedom, etc.   The mass and stiffness matrices in the assembled equation of motion may be uncoupled using the normal modes for the undamped system.  This approach gives real natural frequencies and real mode shapes.

Damping effects can be included in forced response analyses by implicitly assuming that the damping matrix can be diagonalized into modal damping coefficients by the undamped modes.   But systems with dashpots in general have damping matrices which cannot be uncoupled in this manner.

The state-space method is useful for modal and forced response analysis of systems with discrete dashpot damping.  This approach yields complex natural frequencies and mode shapes, with real and imaginary components.

Here is a paper:

Two-Degree-of-Freedom System, State-Space Method:   two_dof_state_space_revC.pdf

More later…

– Tom Irvine

Damping Identification from Shock Data via Wavelet Responses


Structural system & component damping can measured via modal testing with applied force excitation.  One excitation method is an impulse hammer test.  Another method is a  small shaker attached to structure via a stinger rod.

Damping can also be measured by mounting the test unit on a shaker table and applying base excitation.

There is a need to estimate component damping from pyrotechnic or pyrotechnic simulation shock tests where the source energy measurements are incomplete or unavailable.  This need may arise because modal and shaker table test data is unavailable.  Furthermore, damping is nonlinear and may be higher for a pyrotechnic shock event than for a modal or shaker table test

A source shock waveform can be modeled by a series of wavelets per Ferebee R , Irvine T, Clayton J, Alldredge D,  An Alternative Method Of Specifying Shock Test Criteria,  NASA/TM-2008-215253.   This method was original develop to characterize space shuttle solid rocket booster water impact shock.  This method can be extended for natural frequency and damping measurement for shock data.

The Wavelet Response Curve-fit Methodology is appropriate for mid and far field shock measurements where modal responses appear in the accelerometer time history data.

The method is implement via the following steps:

  • Assume a series of wavelet as the base input
  • Calculate the response of one or more SDOF systems to the assumed wavelet series
  • Subtract the resulting response signal from the measured accelerometer data and calculate error
  • The goal is to repeat this process thousands of times where the to minimize the residual error
  • Each of the following parameter are varied randomly with convergence
  • For each base input wavelet: frequency, amplitude, number of half-sines, delay
  • For each SDOF oscillator response: natural frequency, damping

The method yields natural frequency and damping estimates for the response acceleration.  It also gives an estimate of the assumed base input source shock.

The method is demonstrated in the following slides.

Slides:  shock_wavelet_damping_revC.pptx

Matlab scripts & sample shock data: Vibrationdata Signal Analysis Package


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Reference Papers:

An Alternative Method Of Specifying Shock Test Criteria:
NASA/TM-2008-215253 & PowerPoint slide overview


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– Tom Irvine