Vibration Analysis of Structures with Composite Materials

Natural Frequencies of Composite Beams: compbeam.pdf

A function for composite beams is included in: Vibrationdata Matlab Signal Analysis Package

The function can be accessed via:

>> vibrationdata > Miscellaneous Functions I > Structural Dynamics > Beam Bending > General Beam Bending, Composite Laminates

Plates & shells later…

– Tom Irvine

Peak Response to Random Vibration with Probability of Exceedance

An important parameter in random vibration analysis is the peak response, which can be the maximum relative displacement, velocity, acceleration, stress or strain. The peak response can then be compared with the threshold for yielding, ultimate failure, etc. The peak is also important for fatigue analysis, particularly for materials with higher exponents. A common approach is to consider that the peak response is 3σ, where 1σ is the standard deviation. But higher responses often occur > 3σ.

This paper presents a method for estimating the peak response for a desire probability of exceedance.  peak_response_random.pdf

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The equation is included in: Vibrationdata Matlab Signal Analysis Package

The function can be accessed via:

vibrationdata > Miscellaneous Function I > SDOF Response: Sine, Random & Miles > SDOF Response: Peak Sigma for Random Base Input > Risk of Overshoot, XRS, URS

This function may also be used for MDOF systems if the positive slope zero-crossing rate is used in place of the natural frequency.

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See also:

European Cooperation for Space Standardization, Mechanical Shock Design and Verification Handbook, ECSS-E-HB-32-25A

Equivalent Static Loads for Random Vibration

– Tom Irvine

European Space Agency Shock Handbook


LV/SC Clampband Release Test

Here is an excellent reference on shock testing and analysis:

European Cooperation for Space Standardization, Space engineering, Mechanical Shock Design and Verification Handbook, ECSS-E-HB-32-25A, 14 July 2015  download link

The Shock Handbook was covered in several presentations at the ESA 2nd Workshop on Spacecraft Shock Environment and Verification, 2015   presentation link

Tom’s Summary Slides

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See also:

SRS Educational Animation

Vibrationdata Matlab Signal Analysis Package

Vibration Testing & Analysis Standard References

Pyrotechnic Shock

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– Tom Irvine

Bird Songs


I made a recording of a bird in my backyard in Madison, Alabama.  The bird was up in a tall pine tree, and I could not see it.  But I was able to identify it from its song with the help of someone on the WhatBird website forum.  It turned out to be a Carolina Wren, which is the State Bird of South Carolina.  The image above is a stock photo of this species.

More bird songs later…

– Tom Irvine

Earthquake Conference


Rocket vehicles mounted on launch stands at Vandenberg AFB, California must be designed and analyzed to withstand potential earthquakes originating on the nearby San Andreas Fault.  The vehicles behave as long, slender cantilever beams prior to liftoff.

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I am going to present a paper at the

16th World Conference on Earthquake Engineering
January 9-13, 2017, Santiago, Chile

The title is:

Seismic Analysis and Testing of Equipment using Historical Strong Motion Data Scaled to Satisfy Shock Response Spectra Specifications.  Preliminary Draft.

This paper has application for launch vehicles, power substations, telecommunication equipment, buildings, etc.

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See also:

Webinar 47 – Shock Response Spectrum Synthesis, Special Topics

Matlab script: Vibrationdata Signal Analysis Package

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– Tom Irvine

Fatigue Group & Conferences


If you are interested in vibration fatigue please send me a reply.

I am creating a mailing list specifically for fatigue. Topics will include rainflow cycle counting, spectral methods, applications, etc.

My current fatigue offerings are posted at:

Also, I am going to present papers at the following upcoming conferences. Please let me know if you will be able to attend one or more. Or I may be able to visit you at your workplace if you are nearby.

ESTECH, Glendale, Arizona, May 2-5, 2016

Spacecraft and Launch Vehicle Dynamic Environments Workshop, El Segundo, California, June 21-23, 2016

MOVIC & RASD 2016, Southampton UK, July 3-6, 2016

European Conference on Spacecraft Structures Materials and Environmental Testing, Toulouse, France, September 27-30, 2016

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Here is paper that Curtis Larsen and I presented in Prague:

A review of spectral methods for variable amplitude fatigue prediction and
new results  download link

3rd International Conference on Material and Component Performance
under Variable Amplitude Loading, VAL2015

Thank you,
Tom Irvine

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

Here is a paper: spectral_methods_MILHDBK5J.pdf

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The example problem in the paper was performed via the Matlab software posted at Matlab GUI package

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See also

Fatigue Damage for a Stress Response PSD

Rainflow Fatigue Cycle Counting



More later….

Tom Irvine


Employment Opportunity: Structural Analysis Engineer – Loads & Dynamics

Structural Analysis Engineer – Loads & Dynamics 3/4

ApplyJob ID 1600001438Date posted 01/29/2016

Location Huntsville, Alabama, United States

Job Description

The Space Launch System (SLS) program with NASA will restore the nation’s capability in manned access to space, including destinations beyond Earth orbit. First flight will occur in 2018. This position performs development, integration, and documentation of advanced structural analysis for NASA’s SLS Core Stage to establish system design.
This position will perform loads and dynamics analysis to assure compliance with structural integrity and stability requirements.  Coordinates with other engineering groups both within Boeing and with the NASA customer to establish system environments. Develops and conducts analysis processes to support loads analysis for the SLS Upper Stage and Core Stage.  Loads analysis includes simulations of both ground and flight events to which the SLS Stages are exposed, and the development of internal loads on secondary structures or components associated with these flight events. Examples include liftoff, ascent (gust/buffet response), base-drive analysis, development of coupled loads models, etc.
Tools used for these simulations include NASTRAN, PATRAN, FORTRAN, and MATLAB. Demonstrated skills with these tools is required. 
Familiar with Femap and/or DMAP is a plus.
Guides development and continuous improvement of analytical processes. Mentors junior engineers, and works under minimal direction. Ability to communicate effectively to management and customer forums.
Some domestic travel may be required.
Boeing is the world’s largest aerospace company and leading manufacturer of commercial airplanes and defense, space and security systems. We are engineers and technicians. Skilled scientists and thinkers. Bold innovators and dreamers. Join us, and you can build something better for yourself, for our customers and for the world.


Multiaxis Fatigue

Here is a preliminary version of a paper that I am going to present at conference in the UK, July 26.  Multiaxis Rainflow Fatigue Methods for Nonstationary Vibration.

Preliminary Slides:  Irvine_multiaxis_fatigue.pptx

The conference is:  MOVIC & RASD 2016

See also:

Rainflow Cycle Counting

In-plane Rectangular Plate Vibration, FEA

More later…

Tom Irvine

In-plane Rectangular Plate Vibration, FEA


I have written a function for calculating the natural frequencies and modes shapes of a rectangular plate undergoing in-plane vibration via the finite element method.

The function is included in the software posted at in the Matlab GUI package.

The function can be accessed via:

vibrationdata > Structural Dynamics > Plates, In-plane

I will post a corresponding paper later…

– Tom Irvine