Webinar 30 – Rectangular Plate Shock & Vibration

PowerPoint Slides: Webinar_30_rectangular_plates.pptx

Audio Visual File:

NESC Academy Rectangular Plate Shock & Vibration – Recommend viewing in Firefox with Sliverlight Plugin

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References:

Leissa, Vibration of Plates

Plate Base Excitation: plate_base_excitation.pdf

The Natural Frequency of a Rectangular Plate Point-Supported at Each Corner: plate_point_corner.pdf

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Matlab script: Vibrationdata Signal Analysis Package

Data files included in the Package zip file:

srs1000G_accel.txt & navmat_spec.psd

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See also: Vibrationdata Webinars

Thank you,

Tom Irvine

Simply-Supported Plate, Bending Modes

sspm4

The Vibrationdata Signal Analysis Package has a function for calculating the natural frequencies of a plate simply-supported about all edges.

The package also has options for calculating the response to base excitation.

Vibrationdata > Structural Dynamics > Plates, Rectangular & Circular > Rectangular Plate, Simply Supported

The formulas are derived in: plate_base_excitation.pdf

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– Tom Irvine

Contact Form:

Bessel Functions in Vibration Analysis

Bessel Function Table: Bessel_functions.pdf

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Tutorials Referencing Bessel Functions

Newton-Raphson Method Applied to Vibration Problems: Newrap.pdf

Longitudinal Vibration of a Tapered Rod: taper_long.pdf

Natural Frequencies of Circular Plate Bending Modes: circular.pdf

An Introduction to Slosh: slosh_intro.pdf

– Tom Irvine

Enveloping Random Vibration PSD Functions

These Matlab scripts determine an optimum envelope for an acceleration power spectral density: envelope_plateau.zip

The optimum envelope is the that which yields the lowest GRMS and Velocity RMS values.

The acceleration is assumed to be the base excitation for an array of independent, parallel single-degree-of-freedom systems. The vibration response spectrum method is used to justify the envelope.  This provides a rational method for peak-clipping.

The damping ratio is fixed at 0.05, equivalent to Q=10. The natural frequency is an independent variable.

The user must input a power spectral density file.

The file must be ASCII text with two columns:

Freq(Hz) PSD(G^2/Hz)

The main script is envelope_plateau.m

The remaining functions are supporting functions.

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The above scripts generate an optimum PSD which has a series of ramps and plateaus.

Here are the original scripts which generate a more free-form PSD: envelope.zip

The main script is envelope.m

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envelope.zip also contains a script:  envelope_srs_psd.m.

This script can be used to derive a PSD to envelop an SRS.  The script uses the Rayleigh distribution to determine the n-sigma peak for each natural frequency based on the the product of the the natural frequency and duration.

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See also:

Optimized PSD Envelope for Nonstationary Vibration

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– Tom Irvine

Natural Frequencies of a Flat Rectangular Plate, Finite Element Method

platefea

These Matlab scripts calculate the natural frequencies and normal modes of a flat rectangular plate via the finite element method: rectangular_plate_fea.zip

rectangular_plate_fea.m is the main script.

The remaining scripts are supporting function.

Rectangular elements are used for the numerical model, but the plotting elements are triangular.

Here is a reference paper: FEA_plate_bending.pdf

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See also:  plate bending frequency

This other page has a Matlab GUI script for calculating the fundamental frequency of a plate using formulas from classical methods.

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– Tom Irvine

Circular & Annular Plate Bending Frequencies

Here is a set of Matlab GUI scripts for calculating the bending frequencies of both homogeneous and honeycomb-sandwich circular plates:  circular_plate.zip

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Here is a set of Matlab GUI scripts for calculating the bending frequencies of both homogeneous and honeycomb-sandwich annular plates:  annular_plate.zip

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Here are reference papers:
circular.pdf
honey.pdf

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See also:

Circular & Annular Plates

Circular Plate Finite Element Analysis with Triangular Elements

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– Tom Irvine

Contact Form:

Rectangular Plate Bending Frequency

Here is a Matlab GUI script for calculating the bending fundamental frequency of a rectangular plate: rectangular_plate_bending.zip

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See also:

Beam Bending Frequencies

Structural Dynamics – Classical Methods Page

– Tom Irvine

Connect with me on LinkedIn

Reciprocal References

I have never formally published any of my papers in a refereed journal or even in an engineering magazine, but others who have done so have referenced my tutorial papers.

I am enclosing samples, which include conference papers, etc.

– Tom Irvine

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Title: NetLander Surface Module mockup testing
Authors: Sproewitz, T., Block, J., Schuetze, R., Arrat, D., & Obst, A.
Journal: Proceedings of the European Conference on Spacecraft Structures, Materials and Mechanical Testing 2005 (ESA SP-581). 10-12 May 2005, Noordwijk, The Netherlands. Edited by Karen Fletcher. Published on CD-Rom, #63.1
http://adsabs.harvard.edu/full/2005ESASP.581E..63S

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Advances in energy harvesting using low profile piezoelectric transducers
Shashank Priya
J Electroceram (2007) 19:165–182
DOI 10.1007/s10832-007-9043-4
(Data that I measured is shown and referenced in Figure 5)
http://link.springer.com/article/10.1007%2Fs10832-007-9043-4?LI=true#page-1

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Methods to Specify Random Vibration Acceleration Environments
That Comply with Force Limit Specifications
Kristin Fitzpatrick & Scot McNeill
http://sem-proceedings.com/25i/sem.org-IMAC-XXV-s11p06-Methods-Specify-Random-Vibration-Acceleration-Environments-that-Comply-with.pdf

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Separation of Sine and Random Components from Vibration Measurements
Charlie Engelhardt, Mary Baker, Andy Mouron, and Håvard Vold
SOUND & VIBRATION/JUNE 2012
http://www.sandv.com/downloads/1206enge.pdf

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Annals of the University of Petroşani, Mechanical Engineering, 12 (2010), 59-64 59
ABOUT THE TRANSITORY REGIME OF THE MINING EXTRACTION MACHINE
IOANA CRĂCIUN, DINU STOICOVICI, MIRCEA HORGOŞ
http://upet.ro/annals/mechanical/pdf/2010/Annals-Mechanical-Engineering-2010-a7.pdf

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Topics in Modal Analysis I, Volume 5
Conference Proceedings of the Society for Experimental Mechanics Series Volume 30, 2012, pp 385-391
Advanced Response Limiting Technique for Lightly Damped Structures

Jordan Silverstein, Erik Wolf
http://link.springer.com/chapter/10.1007%2F978-1-4614-2425-3_35?LI=true

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Brazilian Journal of Chemical Engineering
Print version ISSN 0104-6632
Braz. J. Chem. Eng. vol.17 n.4-7 São Paulo Dec. 2000
LEAK DETECTION IN PIPELINES THROUGH SPECTRAL ANALYSIS OF PRESSURE SIGNALS
A.L. Souza, S.L.Cruz and J.F.R. Pereira
(See Acknowledgement)
http://www.scielo.br/scielo.php?pid=S0104-66322000000400020&script=sci_arttext

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Innovative Computing Technology, Communications in Computer and Information Science Volume 241, 2011, pp 30-36
Fault Diagnosis of Journal-Bearing of Generator Using Power Spectral Density and Fault Probability Distribution Function
Hojjat Ahmadi, Ashkan Moosavian
http://link.springer.com/chapter/10.1007%2F978-3-642-27337-7_4?LI=true

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Journal of Obesity
Volume 2011 (2011), Article ID 398918, 8 pages
Utility of Accelerometers to Measure Physical Activity in Children Attending an Obesity Treatment Intervention
Wendy Robertson,Sarah Stewart-Brown,Elizabeth Wilcock,Michelle Oldfield, and Margaret Thorogood
http://www.hindawi.com/journals/jobes/2011/398918/ref/

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IVSS-2006-
A New Terrain Sensing System (TSS) based on fatigue damage spectra
Dr. Andrew Halfpenny
http://www.ncode.com/fileadmin/mediapool/nCode/downloads/Whitepaper_nCode_ANewTerrainSensingSystem_Halfpenny.pdf

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New Techniques for Vibration Qualification of Vibrating Equipment on Aircraft
Dr. Andrew Halfpenny, Chief Technologist, HBM-nCode Products
Mr. T. C. Walton, Principal Dynamicist, AgustaWestland
http://www.ncode.com/fileadmin/mediapool/nCode/downloads/GlyphWorks/Whitepaper_nCode_NewTechniques4VibrationQualifonAircraft_AHP_042009AA_S.pdf

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Title: Development of a simulation process of the behaviour of space equipment subjected to pyrotechnic shocks, based on characterization and environmental tests
Authors: Sutra, M., Mesnier, D., Berlioz, A., & Combes, B.
Journal: Proceedings of the European Conference on Spacecraft Structures, Materials and Mechanical Testing 2005 (ESA SP-581). 10-12 May 2005, Noordwijk, The Netherlands. Edited by Karen Fletcher. Published on CD-Rom, #126.1
http://adsabs.harvard.edu/full/2005ESASP.581E.126S

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THE SOCIETY FOR WIND VIGILANCE WIND TURBINE NOISE, SLEEP AND HEALTH
Dr Christopher Hanning. BSc, MB, BS, MRCS, LRCP, FRCA, MD
April 2010
http://www.kolding.dk/pdf/20111031145913.pdf

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Experimental Vibration Analysis of a Composite UAV Wing
Mechanics of Advanced Materials and Structures
Volume 19, Issue 1-3, 2012
J. Simsiriwonga & R. Warsi Sullivan
http://www.tandfonline.com/doi/abs/10.1080/15376494.2011.572248

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Vibration Testing of a Carbon Composite Fuselage
J. Simsiriwong and R. W. Sullivan
Department of Aerospace Engineering
Mississippi State University, Mississippi State, MS 39762
American Society for Composites, 23rd Technical Conference
Memphis, TN, 9-11 September, 2008

https://cavs.msstate.edu/publications/docs/2008/09/5639ASC%202008%20Paper.pdf

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Sensing in Coin Discriminators
Alfonso Carlosena1, Antonio J López-Martín, Fernando Arizti, Ane Martínez-de-Guerenu,
José L. Pina-Insausti, J. Miguel García-Sayés
http://www.csm.unavarra.es/Publicaciones/Images/Pub291.pdf

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Further Developments in the Electromagnetically Sustained Rhodes Piano
Greg Shear & Matthew Wright
http://www.eecs.umich.edu/nime2012/Proceedings/papers/284_Final_Manuscript.pdf

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TRANSIENT DYNAMIC RESPONSES OF AN INTERNAL LIQUID-LNG TANK-SEA WATER INTERACTION SYSTEM
EXCITED BY WAVES AND EARTHQUAKE LOADS
Y. P. Xiong, J. T. Xing and M. Tan
ICSV14   Cairns • Australia 9-12 July, 2007
http://www.acoustics.asn.au/conference_proceedings/ICSV14/papers/p566.pdf

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Target Modes in Moving Assemblies of Compression Drivers and other Speakers
Fernando Bolaños and Pablo Seoane
Audio Engineering Society
Convention Paper, Presented at the 125th Convention
2008 October 2-5 San Francisco, CA, USA
http://profesional.beyma.com/ingles/clipping_aes/AES_125_2008_SAN%20FRANCISCO%20Target%20Modes%20in%20Moving%20Assemblies.pdf

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Natural Frequency Statistics of an Uncertain Plate
Surasak Patarabunditkul
3156945
Bachelor of Engineering (Mechatronic)
June 2009
Supervisor Dr Nathan Kinkaid
http://www.varg.unsw.edu.au/Assets/link%20pdfs/thesis_surasak.pdf

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Assessment of the modes of failure of retaining structures from previous major earthquakes: Caltrans Seismic Design Analysis of Retaining Walls Project
Tadei Shayo    NEES REU 2009
http://nees.org/site/resources/pdfs/REU2009_Tadei_Paper.pdf

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Analysis and Design of Marine Structures: Proceedings of Marstruct 2009, the 2nd International Conference on Marine Structures, Lisbon, Portugal, 16 – 18 March 2009
By Carlos Guedes Soares

http://books.google.com/books/about/Analysis_and_Design_of_Marine_Structures.html?id=0Uxbg6zomSQC

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FILTERING TECHNIQUES APPLIED ON RAW CARRIER PHASE FOR GPS DETECTING SMALL DYNAMIC DISPLACEMENTS
ANA PAULA C. LAROCCA, RICARDO ERNESTO SCHAAL
Boletim de Ciências Geodésicas, Vol. 16, No 1 (2010)
http://ojs.c3sl.ufpr.br/ojs2/index.php/bcg/article/view/17251/11357

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Chromoacoustics: The Science of Sound and Color
John S. Sultzbaugh, Ph.D.
http://rosecroixjournal.org/issues/2009/articles/vol6_94_132_sultzbaugh.pdf

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Recoil Effect of the Ice Hockey Stick During a Slap Shot
A.Villaseñor, R.A. Turcotte, and D.J. Pearsall
McGill University
http://twik.cs.free.fr/index.php/download:/Divers/05Pearsall200_209.pdf

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Mass properties factors in achieving stable imagery from a gimbal mounted camera
Daniel R. Otlowski, Kurt Wiener, Brandon A. Rathbun
Space Electronics LLC, 81 Fuller Way, Berlin, CT, USA 06037
http://www.space-electronics.com/Literature/MP_Factors_in_Stable_Gimbals.pdf

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Resonance in Bottles with Different Shapes
Amy Elliott,  ISB Journal of Physics, January 2012,
http://www.isb.ac.th/HS/JoS/vol6iss2/Papers/2Kendo.pdf

Fixed-Free-Fixed-Free Plate, Fundamental Vibration Mode

The plate is aluminum, 0.063 inch thick.  The fixed edge length is 6 inch.  The free edge length is 4 inch.

The vibration mode was calculated via the Rayleigh method using an assumed displacement function, as carried out via Matlab script:  fixed_free_fixed_free_plate.m

The method is given in:  fixed_free_fixed_free_plate.pdf

See also: Vibrationdata Rectangular Plates

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See also:

Natural Frequencies of a Flat, Rectangular Plate, Finite Element Method

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– Tom Irvine