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The Sonelastic^{®}Solutions are designed to simultaneous characterization of the elastic modulus and damping (internal friction) of materials. Example of publications that used Sonelastic^{®}Solutions. A. H. A. Pereira, G. M. Fortes , B. Schickle, T. Tonnesen, B Musolono, C. D. Maciel, J. A. Rodrigues; "Correlation between changes in mechanical strength and damping of a high alumina refractory castable progressively damaged by thermal shock". Cerâmica 56 (2010) 311314.Standards met by the Sonelastic^{®}Solutions Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance; designation: ASTM E1875. ASTM International.  Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Impulse Excitation of Vibration; designation: ASTM E1876. ASTM International.  Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio of Refractory Materials by Impulse Excitation of Vibration; designation: ASTM C1548. ASTM International.  Standard Test Method for Fundamental Transverse, Longitudinal, and Torsional Frequencies of Concrete Specimens; designation: ASTM C215. ASTM International.  Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio for Advanced Ceramics by Impulse Excitation of Vibration; designation: ASTM C1259. ASTM International.  Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio for Glass and GlassCeramics by Resonance; designation: ASTM C623. ASTM International.  Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio For Ceramic Whitewares by Resonance; designation: ASTM C848. ASTM International.  Standard Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance; designation: ASTM C747. ASTM International. Related references to the equations and calculations used in the Sonelastic^{®}Solutions.For bars and cylinders:  S. P. Timoshenko; On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars. Phil. Mag. Ser. 6 [41] 774746 (1921).  S. P. Timoshenko; On the Transverse Vibrations of Bars of Uniform Cross Section. Phil. Mag. Ser. 6 [43] 125131 (1922).  S. P. Timoshenko; Vibration Problems in Engineering. 2nd Ed. D. Van Nostrand Co., New York, 337342 (1937).  F. Z. Forster; Ein neues Meverfahren zur Bestimmung des Elastizitätsmoduls und der Dämpfung. Zeitschrift Für Metallkunde. v. 29, n. 109 (1937).  G. Pickett; Equations for Computing Elastic Constants from Flexural and Torsional Resonant Frequencies of Vibration of Prisms and Cylinders; Proceedings ASTM, 45 846865 (1945).  S. Spinner, 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).  T. Kaneko; Relation Between Flexional Resonant Frequency Equations for the Flexional Vibration of Cilindrical Rods. J. Res. Natl. Bur. Stand., v. 64B, p. 237 (1960).  Resonance Frequencies of Uniform Bars. J. Res. of the National Bureau of StandardsA. Physics and Chemistry, 64A [2] 147155 (1960).  S. Spinner, W. E. Tefft; A Method for Determining Mechanical Resonance Frequencies and for Calculating Elastic Moduli from these Frequencies. Proceedings ASTM, 61 12211239 (1961). For discs:  J. A. Salem, A. Singh; Polynomial Expressions for Estimating Elastic Constants from the Resonance of Circular Plates. Materials Science and Engineering, A, 422 [1] 292–297 (Apr 2006).  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] 116127 (1965). For plates:  A. W. Leissa, Y. Narita; Vibrations of Completely Free Shallow Shells of Rectangular Planform. J. Sound &Vib. 96 [2] 207218 (1984).  A. A. Wereszczak, R. H. Kraft, J. J. Swab; Flexural And Torsional Resonances Of Ceramic Tiles Via Impulse Excitation Of Vibration; Ceramic Engineering and Science Proceedings, 24 (2003).  T. Lauwagie, H. Solb, G. Roebbenc, W. Heylena, Y. Shib, O. V. der Biest; Mixed numerical–experimental identification of elastic properties of orthotropic metal plates. NDT&E International, 36 487–495 (2003).  M. Alfanol L. Pagnotta; An Inverse Procedure for Determining the Material Constants of Isotropic Square Plates by Impulse Excitation of Vibration. Appl. Mech. Mat., 34 287292 (2005).  M. Alfanol L. Pagnotta; Measurement of the Dynamic Elastic Properties of a Thin Coating. Review of Scientific Instruments, 77 056107 (2006). For discs and rings (grinding wheels):  N. Raju; Vibrations of Annular Plates. J. Aeron. Soc. India, 14 [2] 3752 (1962).  J. Peters, R. Snoeys; The E modulus , a suitable characteristic of grinding wheels. Revue M, II [4] 111 (1965).  S. M. Vogel, D. W. Skinner; Natural Frequencies of Transversely Vibrating Uniform Annular Plates. J. Appl. Mech., 32 926931 (1965).  R. D. Blevins; Formulas for Natural Frequency and Mode Shape. Publ. Krieger Publishing Company (1979).  R. L. Smith; The Evaluation of NDT Techniques for Abrasive Wheels. British Journal of NonDestructive Testing; vol. 28, no2, pp. 7379 (1986). Some references related to the techniques employed in the Sonelastic^{®}Solutions, which are based on natural frequencies of vibration: N. Suansuwan, M. V. Swain; Determination of elastic properties of metal alloys and dental porcelains. J. Oral Rehabilitation, 28 133139 (2001).  H. D. Tietz, M. Dietz, L. Bühling, B. May; NonDestructive Testing of Green Ceramic Materials. NDT.net 3 [11] 17 (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. S. Maxwell, S. OwenJones, N. M. Jennett; Measurement of Young's modulus and Poisson's ratio of thin coatings using impact excitation and depthsensing indentation. Rev. Sci. Instrum. 75 [4] 970975 (2004).  J. Schrooten, G. Roebben, J. A. Helsen; Young's Modulus of Bioactive Glass Coated Oral Implants: Porosity Corrected Bulk Modulus Versus Resonance Frequency Analysis. Scripta Materialia, 41 [10] 10471053 (1999).  C. Chiu, E. D. Case; Elastic Modulus Determination of Coating Layers as Applied to Layered Ceramic Composites. Materials Science and Engineering, A132 3947 (1991). C. Y. Wei, S. N. Kukureka; Evaluation of damping and elastic properties of composites and composite structures by the resonance technique. J. Mat. Sci., 35 37853792 (2000).  B. Christaras, F. Auger, E. Mosse; Determination of the moduli of elasticity of rocks. Comparison of the ultrasonic velocity and mechanical resonance frequency methods with direct static methods. Materials and Structures; Volume 27, n4, pp. 222228 (1994).  A. FAWZY, C.E. SEMLER; Prediction of Refractory Strength Using Nondestructive Sonic Measurements, Am. Ceram. Soc. Bull., v. 64, n. 12, p. 15551558 (1985).  T. Tonnesen, R. Telle; Thermal Shock Damage in Castables: Microstructural Changes and Evaluation by a Damping Method. Ceramic Forum International, v. 84, n. 9, p. E132E136 (2007).  R. Zhang, J. Perez, E. J. Lavernia; Documentation of damping capacity of metallic, ceramic and metalmatrix composite materials. Journal of Materials Science, v. 28, n. 9, p. 23952404 (1993).  R. Morrel; Measuring Elastic Properties of Advanced Technical Ceramics – A review. UK National Physical Laboratory Report, n. 42 (1996).  R. Morrel; NPL Measurement Good Practice Guide  Elastic Module Measurement. UK National Physical Laboratory Report, n. 98 (2006).  T. Akashi; On the Measurement of Logarithmic Decrement of Concrete. General Meeting Reviews, Cement Association of Japan. p. 103104 (1960).  R.N. Swamy; Damping Mechanisms in Cementitious Systems. Proceedings of a Conference on Dynamic waves in civil engineering, University College, Swansea, July 1970; WileyInterscience, p. 521542 (1971).  R.N. Swamy, G. Rigby; Dynamic properties of hardened paste, mortar and concrete. Materials and Structures: Research and Testing. v. 4, n. 19, p. 1340 (1971).  R. Dieterle, H. Banchmann; Experiments and Models for the Damping Behaviour of Vibrating Reinforced concrete Beams in the Uncracked and Cracked Condition.  International Association for Bridge and Structural Engineering Report of the working comissions, v. 34 (1981). 