• Paul A. Bosomworth, " Monitoring the Elastic Properties of Green Ceramics during Firing," Ceramic Industry (February 2016)

• P. C. Chen and D. Rabin, "Carbon nanotube optical mirrors," J. Astron. Telesc. Instrum. Syst., 1 [1], 014005 (2014)

• Igor Stubna, Frantisek Chmelık, Anton Trnık, Peter Sin, “Acoustic Emission Study of Quartz Porcelain during Heating up to 1150°C,” Ceram. Int., 38 6919–6922 (2012)

• Igor Stubna, Frantisek Chmelık, Anton Trnık, Josef Pesicka, “Creation of Microcracks in Porcelain during Firing,” J. Eur. Ceram. Soc., 31 2205-2209 (2011)

• R. Bureš, M. Fáberová, P. Kollár, J. Füzer, M. Strečková , "Microstructure and Fracture of Magnetic Composites with Vitroperm Addition," Powder Metallurgy Progress, 12 [3], 181-186 (2012)

• Paul A. Bosomworth, "Improved Frequency Equations for Calculating the Young’s Modulus of Bars of Rectangular or Circular Cross Section from Their Flexural Resonant Frequencies," J. ASTM International, 7 [8] 1-15 (2010)

• Paul A. Bosomworth and Pierre-Alexis Anctil, "Using IET to Reduce Production Costs," Ceramic Industry, 10-11 (November 2009)

• S. Biswas, T. Nithyanantham, N. T. Saraswathi, and S. Bandopadhyay, "Evaluation of elastic properties of reduced NiO-8YSZ anode supported bi-layer SOFC structures at elevated temperatures in ambient air and reducing environments," J Mater Sci. 44 778-–785 (2009)

• John A. Rice and Abigail Rice, "Young's Modulus and Thermal Expansion of FIlled Cyanate Ester and Epoxy Resins," presented at the Applied Superconductivity Conference, Chicago IL (August 2008)

• H. Windsheimer, N. Travitzky, A. Hofenauer, and P. Greil, "Laminated Object Manufacturing of Preceramic-Paper-Derived Si-SiC Composites," Adv. Mater. 19 [24] 4515-4519 (2007)

• Paul A. Bosomworth, "Predicting Refractory Failure," Ceramic Industry, (October, 2006)

• Christian A. Rottmair, J. Bauer, M. Gruhl, A. Volek, R. F. Singer, "Influence of pressure and heating rate on the mechanical properties of Mesophase based sintered parts," Advances in Science and Technology, 45 584-589 (2006)

• R. Melcher, S. Martins, N. Travitzky, and P. Greil, "Fabrication of Al2O3-based composites by indirect 3D-printing," Materials Letters 60 [4] 572-575 (2005)

• Jürgen Zeschky, Jason Loc, Thomas Höfner, Peter Greil, "Mg alloy infiltrated Si-O-C ceramic foams," Materials Science and Engineering A403 215-221 (2005)

• Paul A. Bosomworth, "An Exciting Technique for Quality Analysis," Ceramic Industry, pp20-24 (February, 2005)

• M. Radovic, E. Lara-Curzio and L. Riester, "Comparison of Different Experimental Techniques for Determination of Elastic Properties of Solids," Materials Science and Engineering, A368 56-70 (2004)

• M. Radovic, and E. Lara-Curzio, "Mechanical properties of tape cast nickel-based anode materials for solid oxide fuel cells before and after reduction in hydrogen," Acta Materialia, 52 5747-5756 (2004)

• J. Zeschky, T. Hoefner, H. Dannheim, M. Scheffler, P. Greil, D. Loidl, S. Puchegger, and H. Peterlik, "High Temperature Behaviour of Ceramic Foams from Si/SiC-Filled Preceramic Polymers," 28 th International Cocoa Beach Conference and Exposition on Advanced Ceramics & Composites (2004)

• "Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration," E1876-09 (2009)

• "Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio of Refractory Materials by Impulse Excitation of Vibration," C1548-02 (2007)

• "Standard Test Method for Fundamental Transverse, Longitudinal, and Torsional Frequencies of Concrete Specimens," C215-08 (2008)

• "Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio for Advanced Ceramics by Impulse Excitation of Vibration," C1259-08e1 (2009)

• "Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio for Glass and Glass-Ceramics by Resonance," C623-92 (2005)

• "Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio For Ceramic Whitewares by Resonance," C848-88 (2006)

• "Standard Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance," C747-93 (2005)

• X. Q. Wang, "The Measurement of Elastic Moduli by Flexural Vibration Testing," Ninth International Congress on Sound and Vibration (Orlando, Florida, USA), 8-11 July (2002)

• N. Suansuwan, and M. V. Swain, "Determination of elastic properties of metal alloys and dental porcelains," J. Oral. Rehab., 28 133-139 (2001)

• H. D. Tietz, M. Dietz, L. Bühling, B. May, "Non-Destructive Testing of Green Ceramic Materials," NDT.net 3 [11] 1-7 (1998)

• W. T. Chu, "A Comparison of Two Test Methods for Measuring Young's Modulus of Building Materials, " Canadian Acoustics, 24 [3] 11 (1996)

• A. Wolfenden, M. R. Harmouche, G. V. Blessing, Y. T. Cjen, P. Terranova, V. Dayal, V. K. Kinra, J. W. Lemmens, R. R. Phillips, J. S. Smith, P. Mahmoodi, and R. J. Wann, "Dynamic Young's Modulus Measurements in Metallic Materials: Results of an Interlaboratory Testing Program," Journal of Testing and Evaluation, JTEVA, 17 [1] 2-13 1989

• J. C. Glandus, F. Platon, and P. Boch, "Measurement of the elastic moduli of ceramics," Materials in Engineering Applications, 1 243-247 (1979)

• A. S. Maxwell, S. Owen-Jones, and N. M. Jennett, "Measurement of Young's modulus and Poisson's ratio of thin coatings using impact excitation and depth-sensing indentation," Rev. Sci. Instrum. 75 [4] 970-975 (2004)

• J. Schrooten, G. Roebben, and J. A. Helsen, "Young's Modulus of Bioactive Glass Coated Oral Implants: Porosity Corrected Bulk Modulus Versus Resonance Frequency Analysis," Scripta Materialia, 41 [10] 1047-1053 (1999)

• L. Chandra and T. W. Clyne, "Use of an Ultrasonic Resonance Technique to Measure the In-plane Young's modulus of Thin Diamond Films deposited by a DC Plasma Jet," Submitted to J. Mat Sci Letts June (1992)

• Chin-Chen Chiu and Eldon D. Case, "Elastic Modulus Determination of Coating Layers as Applied to Layered Ceramic Composites," Materials Science and Engineering, A132 39-47 (1991)

• C. Y. Wei, and S. N. Kukureka, "Evaluation of damping and elastic properties of composites and composite structures by the resonance technique," J. Mat. Sci., 35 3785-3792 (2000)

• G. Roebben, B. Bollen, A. Brebels, J. Van Humbeek, O. Van Der Biest, "Impulse excitation apparatus to measure resonant frequencies, elastic moduli and internal friction at room and high temperature," Review of Scientific Instruments, 68 4511-4515 (1997)

• Kolluru S. V., Popovics, J. S., and Shah, S. P., "Determining Elastic Properties of Concrete Using Vibrational Resonance Frequencies of Standard Test Cylinders," Cement, Concrete, and Aggregates, CCAGDP, 22 [2] 81-89 (2000)

• B. Weiler, and C. Grosse, "Elastic constants - their dynamic measurement and calculation," Otto-Graf-Journal 6 116-131 (1995)

• E. Schreiber, O. Anderson, and N. Soga, "Dynamic Resonance Method for Measuring the Elastic Moduli of Solids, Elastic Constants and their Measurement," 82 - 125, McGraw Hill (1973)

• A. Spinner, and W. E. Tefft, "A Method for Determining Mechanical Resonance Frequencies and for Calculating Elastic Moduli from these Frequencies," Proceedings ASTM, 61 1221-1239 (1961)

• S. Spinner, T. W. Reichard, and W. E. Tefft, "A Comparison of Experimental and Theoretical Relations Between Young's Modulus and the Flexural and Longitudinal Resonance Frequencies of Uniform Bars," J. Res. of the National Bureau of Standards-A. Physics and Chemistry, 64A [2] 147-155 (1960)

• S. Spinner and R. C. Valore, "Comparisons Between the Shear Modulus and Torsional Resonance Frequencies for Bars and Rectangular Cross Sections," Journal of Research, NIST, JNBAA, 60 RP2861, p. 459 (1958)

• G. Pickett, "Equations for Computing Elastic Constants from Flexural and Torsional Resonant Frequencies of Vibration of Prisms and Cylinders," Proceedings ASTM, 45 846-865 (1945)

• D. Bancroft, "The Velocity of Longitudinal Waves in Cylindrical Bars," Phys. Rev., 59 588 (1941)

• S. P. Timoshenko, "Vibration Problems in Engineering," 2nd Ed. D. Van Nostrand Co., New York, 337-342 (1937)

• E. Goens, "Euber die Bestimmung des Elastizitätsmoduls von Stäben mit Hilfe von Biengungsschwingungen," Annalen der Physik, B. Folge, Band 11 649-678 (1931)

• Daniel J. Gorman, "Free Vibration Analysis of Beams and Shafts," Publ. John Wiley and Sons (1975, originally published 1930)

• S. P. Timoshenko, "On the Transverse Vibrations of Bars of Uniform Cross Section," Phil. Mag. Ser. 6 [43] 125-131 (1922)

• S. P. Timoshenko, "On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars," Phil. Mag. Ser. 6 [41] 774-746 (1921)

• Jonathan A. Salem, Abhishek Singh, “Polynomial Expressions for Estimating Elastic Constants from the Resonance of Circular Plates,” Materials Science and Engineering, A, 422 [1] 292–297 (Apr 2006)

• J. C. Glandus, "Rupture fragile et resistance aux choces thermiques d cèramiques à usages mècaniques," Ph.D. Dissertation, University of Limoges (1981)

• J. C. Glandus, F. Platon, and P. Boch, "Measurement of the Elastic Moduli of Ceramics", Materials in Engineering Applications, 1 243-247 (June 1979)

• G. Martincek, "The Determination of Poisson's Ratio and The Dynamic Modulus of Elasticity from the Frequencies of Natural Vibration in Thick Circular Plates," J. Sound Vib., 2 [2] 116-127 (1965)

• M. Alfano and L. Pagnotta, "Measurement of the Dynamic Elastic Properties of a Thin Coating," Review of Scientific Instruments, 77 056107 (2006)

• M. Alfano and L. Pagnotta, "An Inverse Procedure for Determining the Material Constants of Isotropic Square Plates by Impulse Excitation of Vibration," Appl. Mech. Mat., 3-4 287-292 (2005)

• Tom Lauwagie, Hugo Solb, Gert Roebbenc, Ward Heylena, Yinming Shib, Omer Van der Biestc, "Mixed numerical–experimental identification of elastic properties of orthotropic metal plates," NDT&E International, 36 487–495 (2003)

• A. A. Wereszczak, R. H. Kraft, and J. J. Swab, "Flexural And Torsional Resonances Of Ceramic Tiles Via Impulse Excitation Of Vibration," Ceramic Engineering and Science Proceedings, 24 (2003) <www.ornl.gov/~webworks/cppr/y2003/pres/116392.pdf>

• S. Hurlebaus, "Nondestructive Evaluation of Composite Laminates," NDT.net 4 [3] (1999)

• Arthur W. Leissa and Y. Narita, "Vibrations of Completely Free Shallow Shells of Rectangular Planform," J. Sound & Vib. 96 [2] 207-218 (1984)

• Arthur W. Leissa, "Vibration of Plates," Acoustical Society of America, Published in 1993; Originally issued by NASA in 1973 (published 1969)

• W. König and H. Föllinger, "Elasticity Modulus of Grinding Wheels and its Impact on their In-Process Behavior, Part 1," DKG, 64 [6/7] 220-224 (1987)

• W. König and H. Föllinger, "Elasticity Modulus of Grinding Wheels and its Impact on their In-Process Behavior, Part 2," DKG, 64 [8/9] 296-300 (1987)

• D. Adriaenssens, R. Aerens, and J. Peters, "Generalized Formulae Incorporating Martincek's Theory," K.U.L., 1-19 (January 1986)

• A. Decneut "New Formulas Improve E-Modulus Calculations Disc-Shaped Bodies and Rectangular or Square Bars," CRIF Report, MC 37 (1970)

• A. Decneut, R. Snoeys, and J. Peters, "Sonic Testing of Grinding Wheels," CRIF Report, MC 36 (1970)

• J. Peters and R. Snoeys, "The E modulus , A suitable characteristic of grinding wheels," Revue M, II [4] 1-11 (1965)

• S. M. Vogel and D. W. Skinner, "Natural Frequencies of Transversely Vibrating Uniform Annular Plates," J. Appl. Mech., 32 926-931 (Dec 1965)

• N. Raju, "Vibrations of Annular Plates," J. Aeron. Soc. India, 14 [2] 37-52 (May 1962)

• R. McMaster "Nondestructive Testing Handbook," New York, Ronald Press Co. Inc. VII (1953)

• S. Timoshenko, "Vibration Problems in Engineering," New York, D. Van Nostrand Co. Inc. (1928)

See solutions for annular plates in Arthur W. Leissa, "Vibration of Plates," Acoustical Society of America, Published in 1993; Originally issued by NASA in 1973 (published 1969)

• Dragan Mančić and Milan Radmanović, "A Numerical Approach To Analysis of Axisymmetric Rings," Mechanics, Automatic Control and Robotics, 4 [16] 141 - 156 (2004)

• Robert D. Blevins, "Formulas for Natural Frequency and Mode Shape," Publ. Krieger Publishing Company, (1979, reprinted 2001)

• James Kirkhope, "Out-of-Plane Vibration of Thick Circular Ring," J. Eng. Mech., 102 [EM2] 239-247 (April 1976)

• Arthur W. Leissa, "Vibration of Shells," Acoustical Society of America, Published in 1993; Originally issued by NASA in 1973

• Arthur W. Leissa, Jinyoung So, "Free Vibrations of Thick Hollow Circular Cylinders From Three-Dimensional Analysis," J. Vib. and Acoustics, 119 89-95 (1997)

• L. Cremer, M. Heckl, and B.A.T. Petersson, "Structure-Borne Sound : Structural Vibrations and Sound Radiation at Audio Frequencies," Springer; 3 edition (March 14, 2005)

• Cyril M. Harris and Allan G. Piersol, "Harris' Shock and Vibration Handbook," 5th Ed., Publ. McGraw-Hill, 2003

• Giancarlo Genta,"Vibration of Structures and Machines," Publ. Springer-Verlag, 1993

• James M. Gere and Stephen P. Timoshenko, "Mechanics of Materials," 2nd Ed., Publ. Brooks/Cole Engineering Division, 1984.

• Robert D. Blevins, "Formulas for Natural Frequency and Mode Shape," Publ. Krieger Publishing Company, (1979, reprinted 2001)

• L. Meirovitch, "Analytical Methods in Vibrations," Macmillan, London, England, 1967

See also Tom Irvine's website (http://www.Vibrationdata.com) and the "Natural Frequencies for Common Systems," at the Modal Analysis and Controls Laboratory of the University of Massachusetts Lowell for general information on vibration analyses.

• Paul A. Bosomworth, "An Exciting Technique for Quality Analysis," Ceramic Industry, February, 2005

• J.P. Erauw, A. Vander Gucht and F. Cambier, "Assessment of Impact Acoustic Resonance as a Non-Destructive Testing Method for Advanced Ceramic Parts," Key Engineering Materials, 264-268 921-924 (2004)

• "Acoustic Testing - Nonlinear Acoustic Testing Techniques, A Form of Nondestructive Testing," AZoM <http://www.azom.com/details.asp?ArticleID=2148>, originally published in Materials World 7 [9] 544-46 (1999)

• T. G. Chondros, A. D. Dimarogonas, and J. Yao "A Continuous Cracked Beam Vibration Theory," J. Sound and Vibration, 215 [1] 17-34 (1998)

• Transnational College of LEX, "Who Is Fourier?," Language Research Foundation, Boston (1995)

• J. P. G. Richards, and R. P. Williams, "Waves," Penguin Books (1972)

• R. Feynman, "The Feynman Lectures on Physics vol. I, II, III," Addison-Wesly (1965)

• W. H. Press, W. T. Vettering, S. A. Teukolsky, and B. P. Flannery, "Numerical Recipes in C," 2nd ed., Cambridge University Press (1996)

• D. F. Elliot, and K. R. Rao, "Fast Fourier Transforms, Algorithms, Analyses, Applications," Academic Press (1982)

• M. L. Chugani, A. R. Samant, and M. Cerna, "LabVIEW Signal Processing," Prentice-Hall PTR, Prentice-Hall, Inc. and Simon & Schuster Company (1998)

Many references and tutorials are given on the National Instruments website

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