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Damping associated with porosity in alumina

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Abstract

Materials subjected to alternating stresses exhibit temperature fluctuations indicative of damping. Temperature effects give rise to entropy production. An analysis is made to obtain the entropy produced for a vibration cycle. This corresponds to the reciprocity of temperature rise and strain yielded that alter the material damping factor as a function of shape and magnitude of material porosity. Prototype bars of pure aluminum oxide with different porosity are considered. They consist of uniformly distributed cavities and are subjected to alternating axial stress. Dynamic characteristics of the porous medium are determined to evaluate the damping factor of the tested bars. The experimental data correlate well with the analytical results. The damping factor measured and calculated in this work, can be used as an indicator of structural integrity.

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Abbreviations

MDF:

Modal damping factor

References

  • Alblas, J.: On the general theory of thermo-elastic friction. Appl. Sci. Res. 10(Sect. A), 349–367 (1961)

  • Alblas, J.: A note on the theory of thermoelastic damping. J. Therm. Stress. 4, 333–355 (1981). doi:10.1080/01495738108909973

    Article  Google Scholar 

  • Armstrong, B.: Models for thermoelastic attenuation of waves in heterogeneous solids. Geophysics 49(7), 1032–1040 (1984). doi:10.1190/1.1441718

    Article  Google Scholar 

  • Bejan, A.: Entropy Generation Through Heat abd Fluid Flow. Wiley, New York (1982)

    Google Scholar 

  • Biot, M.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27(3), 240–253 (1956). doi:10.1063/1.1722351

    Google Scholar 

  • Bishop, J., Kinra, V.: Some improvements in the flexural damping measurement technique. In: Kinra, V.K., Wolfenden, A. (eds.) M3D: Mechanics and Mechanisms of Material Damping, ASTM STP 1169, pp. 457–470. American Society for Testing and Materials, Philadelphia, Pennsylvania (1992)

  • Bishop, J., Kinra, V.: Thermoelastic damping of a laminated beam in flexure and extension. J. Reinf. Plast. Compos. 12, 210–226 (1993a). doi:10.1177/073168449301200207

    Article  Google Scholar 

  • Bishop, J., Kinra, V.: Elastothermodynamic damping of metal-matrix composites. Thermodynamics and the design and improvement of energy systems AES-vol. 30, HTD-vol. 266. In: Richter, H.J. (ed.) Proceedings of the 1993 Winter Annual Meeting, pp. 127–138 (1993b)

  • Bishop, J., Kinra, V.: Elastothermodynamic damping in particle-reinforced metal-matrix composites, AES-vol. 33. ASME (1994)

  • Coleman, B.D., Mizel, V.J.: Existence of caloric equations of state thermodynamics. J. Chem. Phys. 40, 1116–1125 (1964). doi:10.1063/1.1725257

    Article  MathSciNet  Google Scholar 

  • Coleman, B.D., Noll, W.: Foundations of linear viscoelasticity. Rev. Mod. Phys. 33, 239–249 (1961). doi:10.1103/RevModPhys.33.239

    Article  MATH  MathSciNet  Google Scholar 

  • Deresiewitcz, H.: Plane waves in a thermoelastic solid. J. Acoust. Soc. Am. 29(2), 204–209 (1957). doi:10.1121/1.1908832

    Article  Google Scholar 

  • Dimarogonas, A.: Vibration for Engineers, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ (1996)

    Google Scholar 

  • Frederick, D., Chang, T.S.: Continuum Mechanics, p. 169. Scientific Publishers, Cambridge, MA (1972)

    Google Scholar 

  • Gillis, W.: Damping of Thermoelastic Structures, Technical Memorandum X-53722. George C. Marshall Space Flight Center, Orbital Mechanics Section, 1968

  • Goodman, L., Chang, C., Robinson, A.: Thermoelastic damping. Technical documentary report no. ASD-TDR-62-1031. Wright-Patterson Air Force Base, Ohio (1962)

  • Gouy, M.: Sur l’energie utilisable. J. Phys. 8, 501 (1889)

    Google Scholar 

  • Kinra, V., Milligan, K.: A second law analysis of thermoelastic damping, ASME 1949. J. Appl. Mech. 61(1), 71–76 (1994). doi:10.1115/1.2901424

    Article  Google Scholar 

  • Landau, L., Lifshitz, E.: Theory of Elasticity. Pergamon Press, New York (1986)

    Google Scholar 

  • Lazan, B.J.: Damping of Materials and Members in Structural Mechanics. Pergamon Press, Oxford (1968)

    Google Scholar 

  • Lee, U.: Thermoelastic and electromagnetic damping analysis. AIAA J. 23(11), 1783–1790 (1985). doi:10.2514/3.9166

    Article  MATH  Google Scholar 

  • Lucke, K.: Ultrasonic attenuation caused by thermoelastic heat flow. J. Appl. Phys. 27(12), 1433–1438 (1956). doi:10.1063/1.1722284

    Article  MathSciNet  Google Scholar 

  • Lyckfeldt, O., Ferreira, J.M.F.: Processing of porous ceramics by “starch consolidation”. J. Eur. Ceram. Soc. 18(2), 131–140 (1998). doi:10.1016/S0955-2219(97)00101-5

    Article  Google Scholar 

  • Milligan, K., Kinra, V.: On the damping of a one-dimensional inclusion in a uniaxial bar. Mech. Res. Commun. 20, 137–142 (1993a)

    Article  MATH  Google Scholar 

  • Milligan, K., Kinra, V.: Elastothermodynamic damping of fiber-reinforced metal-matrix composites, thermodynamics and the design and improvement of energy systems AES-vol. 30, HTD-vol. 266. In: Richter, H.J. (ed.) Proceedings of the 1993 Winter Annual Meeting, pp. 139–148 (1993b)

  • Nowacki, W.: Thermoelasticity. Pergamon Press, New York (1962)

    Google Scholar 

  • Ozisik, M.: Necati, Heat Conduction, 2nd edn. Wiley, NY (1993)

    Google Scholar 

  • Panteliou, S.D., Dimarogonas, A.D.: Thermodynamic damping in porous materials with ellipsoidal cavities. J. Sound Vib. 201(5), 555–565 (1997). doi:10.1006/jsvi.1996.0784

    Article  Google Scholar 

  • Panteliou, S.D., Dimarogonas, A.D.: Damping associated with porosity and crack in solids. Theor. Appl. Fract. Mech. 34(3), 217–223 (2000)

    Article  Google Scholar 

  • Sadowski, M.A., Sternberg, E.: Stress concentration around a triaxial ellipsoidal cavity. J. Appl. Mech. 16, 149–157 (1949). Paper No. 48-A-29

    Google Scholar 

  • Shieh, R.: Thermoelastic Damping and it’s Effect on Flutter of Stressed Panels Situated in a Supersonic Airflow, NASA TND-6448. NASA Langley Research Center, Hampton, Virginia (1971)

  • Shieh, R.: Thermoelastic vibration and damping for circular timoshenko beams. ASME J. Appl. Mech. 42(2), 405–410 (1975)

    Google Scholar 

  • Shieh, R.: Eigensolutions for coupled thermoelastic vibrations of timoshenko beams. ASME J. Appl. Mech. 46, 169–174 (1979)

    MATH  Google Scholar 

  • Stodola, A.: Steam and Gas Turbines. McGraw-Hill, New York (1910)

    Google Scholar 

  • Tasi, J.: Thermoelastic dissipation in vibrating plates. J. Appl. Mech. 30, 562–567 (1963)

    MATH  Google Scholar 

  • Tasi, J.G.: Herrmann. J. Acoust. Soc. Am. 36(1), 100–110 (1964). doi:10.1121/1.1918920

    Article  MathSciNet  Google Scholar 

  • Timoshenko, S., Goodier, J.N.: Theory of Elasticity, 2nd edn. McGraw-Hill, New York (1951)

    MATH  Google Scholar 

  • Zemansky, M., Dittman, R.: Heat and Thermodynamics, 6th edn. McGraw-Hill, New York (1981)

    Google Scholar 

  • Zener, C.: Internal friction in solids. I. Theory of internal friction in reeds. Phys. Rev. 52, 230–235 (1937). doi:10.1103/PhysRev.52.230

    Google Scholar 

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Panteliou, S.D., Zonios, K., Chondrou, I.T. et al. Damping associated with porosity in alumina. Int J Mech Mater Des 5, 167–174 (2009). https://doi.org/10.1007/s10999-008-9092-0

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