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.
Similar content being viewed by others
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
Armstrong, B.: Models for thermoelastic attenuation of waves in heterogeneous solids. Geophysics 49(7), 1032–1040 (1984). doi:10.1190/1.1441718
Bejan, A.: Entropy Generation Through Heat abd Fluid Flow. Wiley, New York (1982)
Biot, M.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27(3), 240–253 (1956). doi:10.1063/1.1722351
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
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
Coleman, B.D., Noll, W.: Foundations of linear viscoelasticity. Rev. Mod. Phys. 33, 239–249 (1961). doi:10.1103/RevModPhys.33.239
Deresiewitcz, H.: Plane waves in a thermoelastic solid. J. Acoust. Soc. Am. 29(2), 204–209 (1957). doi:10.1121/1.1908832
Dimarogonas, A.: Vibration for Engineers, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ (1996)
Frederick, D., Chang, T.S.: Continuum Mechanics, p. 169. Scientific Publishers, Cambridge, MA (1972)
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)
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
Landau, L., Lifshitz, E.: Theory of Elasticity. Pergamon Press, New York (1986)
Lazan, B.J.: Damping of Materials and Members in Structural Mechanics. Pergamon Press, Oxford (1968)
Lee, U.: Thermoelastic and electromagnetic damping analysis. AIAA J. 23(11), 1783–1790 (1985). doi:10.2514/3.9166
Lucke, K.: Ultrasonic attenuation caused by thermoelastic heat flow. J. Appl. Phys. 27(12), 1433–1438 (1956). doi:10.1063/1.1722284
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
Milligan, K., Kinra, V.: On the damping of a one-dimensional inclusion in a uniaxial bar. Mech. Res. Commun. 20, 137–142 (1993a)
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)
Ozisik, M.: Necati, Heat Conduction, 2nd edn. Wiley, NY (1993)
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
Panteliou, S.D., Dimarogonas, A.D.: Damping associated with porosity and crack in solids. Theor. Appl. Fract. Mech. 34(3), 217–223 (2000)
Sadowski, M.A., Sternberg, E.: Stress concentration around a triaxial ellipsoidal cavity. J. Appl. Mech. 16, 149–157 (1949). Paper No. 48-A-29
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)
Shieh, R.: Eigensolutions for coupled thermoelastic vibrations of timoshenko beams. ASME J. Appl. Mech. 46, 169–174 (1979)
Stodola, A.: Steam and Gas Turbines. McGraw-Hill, New York (1910)
Tasi, J.: Thermoelastic dissipation in vibrating plates. J. Appl. Mech. 30, 562–567 (1963)
Tasi, J.G.: Herrmann. J. Acoust. Soc. Am. 36(1), 100–110 (1964). doi:10.1121/1.1918920
Timoshenko, S., Goodier, J.N.: Theory of Elasticity, 2nd edn. McGraw-Hill, New York (1951)
Zemansky, M., Dittman, R.: Heat and Thermodynamics, 6th edn. McGraw-Hill, New York (1981)
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10999-008-9092-0