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

Damping References


Structural damping depends on materials, joints, boundary conditions, friction, acoustic radiation, etc.  Damping may be nonlinear, increasing as the excitation and response levels rise. The damping for a given structure or component must be measured!  

But here is some empirical background data…


Damping Properties of Materials

Damping Cross-Reference

Damping Values in Aerospace Structures and Components

Free Vibration with Coulomb Damping

Damping Identification Rev A

Related Blog Posts

Honeycomb Sandwich Panels

Vibroacoustics/Statistical Energy Analysis  – empirical formulas for loss factors

Wire Rope Cable Damping

Tall Building Natural Frequencies and Damping

Piezoelectric Shunt Damping

Nonlinear Modeling of Bolted Interfaces & Joints

Convert Modal Damping to a Damping Coefficient Matrix

Vibration Absorbers & Tuned Mass Dampers

Half-Power Bandwidth Method


Isolator Photo Gallery

Avionics Box Isolation

Transmissibility of a Three-Parameter Isolation System

Webinar 43 – Two-degree-of-freedom System, Two-stage Isolation

– Tom Irvine

Engineering Status Reports

For the past eight years, I have written a required monthly status report to another organization for my NASA contractor work. I have written my accomplishments and planned work in short, concise sentences, usually in numbered list format.

I was then notified by this organization that the writing rules had been changed substantially. The new rules prohibited bullet or numerical list format. Personal pronouns could no longer be used. The sentences must be varied to avoid beginning each with the subject. The writing had to be in paragraph format with three sentences per paragraph, and on and on. There were so many new rules that I did not even read all of them. I wondered if perhaps an English literature major had been given an administrative role and was projecting his or her frustrations by imposing Byzantine writing style rules upon myself and others in this technical community.

So I submitted the following status report, with slight edit changes to avoid disclosing any proprietary information. I refer to myself in third person as the “greybeard.”

The organization responded by instructing me to return to my previous, concise writing style for the status reports, exempting me from the new rules.

And I really did give a presentation to NASA engineers that included a slide about monkeys SLaMS_SCLV201_keynote_revA.ppt

– Tom Irvine

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Significant Accomplishments:

Dynamics Engineering: A Call to Serve! Enlightened were the apprentices as the greybeard mentored them with this presentation at the SLaMS Early Career Community webinar meeting, March 27, calling upon them to share their knowledge and become themselves teachers of the rising generation, underscored with Seneca the Younger’s proverb Docendo discimus – Latin “by teaching, we learn.” Reciprocal altruism of Vervet monkeys! Blind Faults underneath the Los Angeles Basin! Dragons to be launched on towering SpaceX boosters powered by Merlin engines! Thus was the eclectic tutelage of that day.

The raw, ominous Zeus-like power of pyrotechnic shock pulses cutting through rocket joint metal, propagating through modules and threatening sensitive electronic parts mounted on circuit boards – such has been the forlorn of many a NASA engineer. To which challenge did the greybeard prepare shock, structural dynamics, fatigue and statistical energy analysis software and training materials as tools for discerning the energy’s spectral content.

Work Planned:

Gathered will be engineers at the NESC Joint GN&C TDT and L&D TDT F2F Meeting at MSFC – week of April 16, 2018, bringing opportunities of collaboration for the greybeard and his esteemed colleagues. New ideas will arise upon which the greybeard will muse, research and present new papers and methodologies, knowing that if he sees farther than others– it is because he stands on the shoulders of giants.

The response of mechanical components bending and flexing in multi-modes driven by the surging oscillations of pyrotechnic shock waves, the stresses pulling molecules apart, potentially inducing cracks which threaten both component and launch vehicle, for which the greybeard is preparing a presentation for the Aerospace Spacecraft and Launch Vehicle Dynamic Environments Workshop, El Segundo, CA, June 26-28, 2018 – this and more are the planned endeavors for the month of April.


Matlab scripts, the tools for synthesizing acceleration time histories across a series of wavelets, the greybeard’s quest to numerically replicate the damage potential of powerful undulations which could break launch vehicle components and structure, will be conveyed to NASA engineers. Tutorials and slides with examples using the scripts will be provided, enabling these ladies and gentlemen to perform calculations of their own in service of America’s space program.

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Here is the bullet version, with no literary allusions.

Significant Accomplishments:

1. Gave presentation “Dynamics Engineering: A Call to Serve!” to the NASA SLaMS Early Career Community via webinar meeting, March 27. Presentation included references to reciprocal altruism of Vervet monkeys and blind faults underneath the Los Angeles basin.
2. Writing avionics component FEA shock analysis software and tutorials for NASTRAN implementation.

Work Planned:

1. Preparation of structural dynamics & statistical energy analysis software & webinars.
2. Prepare presentation for the Aerospace Spacecraft and Launch Vehicle Dynamic Environments Workshop, El Segundo, CA, June 26-28, 2018. Presentation title is Avionics Component FEA Shock Analysis.
3. Participate in the NESC Joint GN&C TDT and L&D TDT F2F Meeting at MSFC.


1. Webinar audio/visual presentation files.
2. Revised Matlab & Python GUI signal analysis packages with enhanced features.
3. Statistical energy analysis, structural dynamics, vibration fatigue software and tutorial papers.

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

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Prerequisite Materials

Webinar Index

Structural Dynamics Webinars

Matlab Vibrationdata GUI

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Main Presentations:

Nastran Modal Transient Slides:  200_FEA_modal_transient_revJ.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 FEA Frequency Response Function for Base Input:  203_FEA_frf_revB.pptx

FEA PSD Response for Base Excitation using Femap, Nastran & Matlab:  204_FEA_psd.pptx

Avionics Component Shock Sensitivity & FEA Shock Analysis:  avionics_box_fea_shock.pptx

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Nastran Files

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







Nastran Acceleration Time History:  srs2000G_accel.nas

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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.

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Note:  the dimension of the extracted mass matrix will be less than that of the stiffness matrix for models with massless nodes.

Here is a workaround:

An Indirect Method for Extracting Nastran Full Mass Matrices for Models with Massless Nodes  extract_massless_node.pdf

– 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

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 middle is the corresponding Waterfall SRS with 4 second segments and with 50% overlap.  The bottom is the spectrogram.

The Waterfall SRS 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 SRS

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