Spatial estimates concerning the harmonic vibrations in rectangular plates with voids

• Autorzy: Ghiba I.-D.
• Języki publikacji: EN

Abstrakty

EN

This paper studies the spatial behaviour of the amplitude of a harmonic vibration in a rectangular plate of Mindlin type, made of a homogeneous and isotropic elastic material with voids. Provided the frequency of vibration is lower than the critical value, some appropriate measures are introduced relating the amplitude of resulting harmonic vibration, and the corresponding first-order differential inequalities are established under mild conditions on the elastic coefficients. The case of a semi-infinite plate is also studied and some Phragmén-Lindelöf alternatives are established.

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2008
• Tom: Vol. 60, nr 3
• Strony: 263--279
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Ghiba I.-D.

• "Octav Mayer" Mathematics Institute Iasi, Romanian Academy of Science Bd. Carol I, nr 8, 700506-Iasi, Romania,

Bibliografia

• 1. J,W. NUNZIATO and S.C, COWIN, A non-linear theory of elastic materials with voids, Arch. Rational Mech. Anal., 72, 175-201, 1979.
• 2. M.A. GOODMAN and S.C. COWIN, A continuum theory for granular materials, Arch. Rational Mech. Anal., 44, 249-266, 1972.
• 3. S.C. COWIN and J.W. NUNZIATO, Linear elastic materials with voids, J. Elasticity, 13, 125-147, 1983.
• 4. D. IESAN, A theory of thermoelastic materials with voids, Acta Mechanica, 60, 67-89, 1986.
• 5. D. IESAN and M. CIARLETTA, Non-classical elastic solids, Longman Scientific and Technical, Harlow, Essex, UK and John Wiley & Sons, Inc., New York 1993.
• 6. D. IESAN, Thermoelastic models of continua, Kluwer Academic Publishers, Boston/Dordrecht/London 2004.
• 7. R.D. MlNDLlN. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, J. Appl. Mech., 18, 31-38, 1951.
• 8. E. REISSNER, On the theory of bending of elastic plates, J. Math. Phys., 23, 184-191, 1944.
• 9. C. CONSTANDA, A mathematical analysis of bending of plates with transverse shear deformation, Langman Scientific & Technical, 1990.
• 10. P. SCHIAVONE and C. CONSTANDA, Oscillation problems in thin plates with transverse shear deformation, SIAM J. Appl. Math., 53, 5, 1253-1263, 1993.
• 11. P. SCHIAVONE and R.J. TAIT, Steady time-harmonic oscillations in a linear thermoelastic plate model, Quart. Appl. Math., LIII, 215-223, 1995.
• 12. M. CIARLETTA, On the spatial behaviour of the transient and steady-state solutions in thin plates with transverse shear deformation, Int. J. Engn. Sci., 40, 485-498, 2002.
• 13. C. D'APICE and S. CHIRITA, Spatial behaviour in a Mindlin-type thermoelastic plate, Quarterly of Applied Mathematics, 61, 783-796, 2003.
• 14. C. D'ApiCE, A mathematical study of the spatial behaviour of the time-harmonic ascilla-tions in a thermoelastic rectangular plate, An. St. Univ. Al. I. Cuza Iasi, ser. Matematica, 51, 9-23, 2005.
• 15. E. SCARPETTA, Minimum principle for the bending problem of elastic plates with voids, Int. J. Engn. Sci., 40, 1317-1327, 2002.
• 16. M. BIRSAN, A bending theory of porous thermoelastic plates, Journal of Thermal Stresses, 26, 67-90, 2003.
• 17. M. BIRSAN, On the bending equations for elastic plates with voids, Math. Mech. Solids, 12, 40-57, 2007.
• 18. M. BlRSAN, Transient and steady-state solutions for porous thermoelastic plates, An. St. Univ A.I. Cuza Iasi, ser. Matematica, 52, 159-176, 2006.
• 19. S. CHIRITA and M. CIARLETTA, Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua, European Journal of Mechanics, A/Solids, 18, 915-933, 1999.
• 20. S. CHIRITA, Further results on the spatial behavior in linear elastodynamics, An. St. Univ. Iasi, ser. Matematica, 50, 289-304, 2004.
• 21. S. CHIRITA, Some growth and decay estimates for a cylinder made of an elastic material with voids, Rev. Roum. Math. Pures et Appl., 39, 17-26, 1994.
• 22. S. CHIRITA, On some exponential decay estimates for porous elastic cylinder, Arch. Mechanics, 56, 199-212, 2004.
• 23. D. IESAN and R. QUINTANILLA, Decay estimates and energy bounds for porous elastic cylinders, Z. angew. Math. Phys., 46, 268-281, 1995.
• 24. M. CIARLETTA, S. CHIRITA and F. PASSARELLA, Some results on the spatial behaviour in linear porous elasticity, Arch. Mechanics, 57, 43-65, 2005.
• 25. R. LAKES, Foam structure with negative Poisson's ratio, Science, 235, 1038-1040, 1987.
• 26. R.S. LAKES, No contractile obligations, Nature, 358, 713-714, 1992.
• 27. R. LAKES, A broader view of membranes, Nature, 414, 503-504, 2001.
• 28. N.K. McGuiRE, Negative-coefficient materials can point the way to positive value in the right matrixes, Today's chemist at work, American Chemical Society, Nov., 24-28, 2002.
• 29. L.B. PARK and R.S. LAKES, Biomaterials, third edition, Springer, 2007.