Fundamental solution in micropolar viscothermoelastic solids with void

• Autorzy: Kumar R. , Sharma K. D. , Garg S. K.

Identyfikatory

DOI

10.1515/ijame-2015-0008

• Języki publikacji: EN

Abstrakty

EN

In the present article, we construct the fundamental solution to a system of differential equations in micropolar viscothermoelastic solids with voids in case of steady oscillations in terms of elementary functions. Some basic properties of the fundamental solution are also established.

Słowa kluczowe

EN

micropolar thermodiffusion; steady oscillations; visothemoelastic; micropolar with void

PL

drgania; termosprężystość; funkcje elementarne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2015
• Tom: Vol. 20, no. 1
• Strony: 109--125
• Opis fizyczny: Bibliogr. 50 poz.

Twórcy

autor

Kumar R.

• Department of Mathematics Kurukshetra University Kurukshetra Kurukshetra, INDIA

autor

Sharma K. D.

• Department of Mathematics Gurukul Vidyapeeth Institute of Engineering and Technology Ramnagar, Banur, Rajpiua (Punjab), INDIA

autor

Garg S. K.

• Department of Mathematics Deenbandhu Chhotu Ram University Murthal (Sonipat), INDIA

Bibliografia

• [1] Aouadi M. (2012a): Uniqueness and existence theorems in thermoelasticity with voids without energy dissipation. – Journal of the Frankline Institute, vol.349, No.1, pp.128-139.
• [2] Aouadi M., Barbara L. and Nibbi R. (2012b): Exponential decay in thermoelastic materials with voids and dissipative boundary without thermal dissipation. – Zeitschrift fur Angewandte Mathamatik und Physik, vol.63, No.5, pp.961-973.
• [3] Chandrasekharaiah D.S. (1987a): Effects of surface stresses and voids on Rayleigh waves in an elastic solid. – Int. J. Engng. Sci., vol.25, pp.205-211.
• [4] Chandrasekharaiah D.S. (1987b): Rayleigh-Lamb waves in an elastic plate with voids. – Trans. ASME. J. Appl. Mech., vol.54, pp.509-512.
• [5] Ciarletta M. and Straughan B. (2007): Thermo-poroacoustic waves in elastic materials with voids. – Journal of Mathematical Analysis and Applications, vol.333, No.1, pp.142-150.
• [6] Cowin S.C. and Nunziato J.W. (1983): Linear elastic materials with voids. – J. Elasticity, vol.13, pp.125-147.
• [7] Dhaliwal R.S. and Wang J. (1994): A domain of influence theorem in the linear theory of elastic materials with voids. – Int. J. Engng. Sci., vol.32, pp.1823-1828.
• [8] Eringen A.C. (1968): Theory of micropolar elasticity. [in:] Fracture, H. Liebovitz [Ed.], vol.5, Academics Press, New York.
• [9] Eringen A.C. (1970): Foundations of micropolar thermoelasticity. – International Centre for Mechanical Science, Course and Lecture . No.23, Springer, Berlin.
• [10] Eringen A.C. (1967): Linear theory of micropolar viscoelasticity. – Int. J. Eng. Sci., vol.5, pp.191-204.
• [11] Eringen A.C. (1999): Micro-continuum Field Theories – I. Foundations and Solids. – Berlin: Springer-Verlag.
• [12] Ezzat M.A. and Atef H.M. (2011): Magneto-thermo-viscoelastic material with a spherical cavity. – Journal of Civil Engineering and Construction Technology, vol.2, No.1, pp.6-16.
• [13] Gale C. (2000): On Saint-Venant’s problem in micropolar viscoelasticity. – An Stiin. Univ. Al I Cuza Iasi Mat., vol.46, pp.131-148.
• [14] Hetnarski R.B. (1964a): The fundamental solution of the coupled thermoelastic problem for small times. – Arch. Mech., Stosow., vol.16, pp.23-31.
• [15] Hetnarski R.B. (1964b): Solution of the coupled problem of thermoelasticity in form of a series of functions. – Arch. Mech., Stosow., vol.16, pp.919-941.
• [16] Hormander L. (1963): Linear Partial Differential Operators. – Berlin: Springer-Verlag.
• [17] Hormander L. (1983): The analysis of Linear Partial Differential operators-II. Differential Operators with Constant Coefficients. – Berlin: Springer-Verlag.
• [18]Iesan D. (1986): A theory of thermoelastic with voids. – Acta Mechanica, vol.60, pp.67-89.
• [19] Iesan D. (2011): On a theory of thermoviscoelastic molecules with voids. – J. Elast., vol.104, pp.369-384.
• [20] Iesan D. and Quintanilla R. (1995): Decay estimates and energy bounds for porous elastic cylinders. – J. Appl. Math. Phys. (ZAMP), vol.46, pp.268-281.
• [21] Kumar R. (2000): Wave propagation in micropolar viscoelastic generalized thermoelastic solid. – Int. J. Eng. Sci., vol.38, pp.1377-1395.
• [22] Kumar R. and Choudhary S. (2001): Dynamical problem of micropolar viscoelasticity. – Proc. Indian Acad Sci.(Earth Planet Sci.), vol.110, pp.215-223.
• [23] Kumar R. and Choudhary S. (2005a): Deformation due to time harmonic source in orthotropic micropolar viscoelastic medium. – Int. J. Appl. Mech. and Eng., vol.10, No.4, pp.617-629.
• [24] Kumar R. and Choudhary S. (2005b): Deformation due to time harmonic source in orthotropic micropolar viscoelastic medium. – Georgian Mathematical Journal, vol.12, pp.261-272.
• [25] Kumar R. and Partap Geeta (2010): Free vibration analysis of waves in microstretch viscoelastic layer. – Applied Mathematics and Information Sciences, vol.4, No.1, pp.107-123.
• [26] Kumar R. and Panchal M. (2011): Study of circular crested waves in a micropolar porous medium possessing cubic symmetry. – Bulletin of the Polish Academy of Technical Sciences, vol.59, No.1, pp.103-110.
• [27] Kumar R., Sharma K.D. and Garg S.K. (2012): Deformation due to various sources in micropolar elastic solid with voids under inviscid liquid half space. – Global Journal of Science Frontier Research, Physics and Space Science, vol.12, No.1, pp.35-44.
• [28] Kumar R. and Kansal T. (2012a): Fundamental solution in the theory of micropolar thermoelastic diffusion with voids. Comput. Appl. Math., vol.31, No.1, pp.169-189.
• [29] Kupradze V.D., Gegelia T.G., Basheleishvili M.O. and Burchuladze T.V. (1979): Three dimensional problems of the mathematical theory of elasticity and thermoelasticity. – North-Holland Pub. Company: Amsterdam, New York, Oxford.
• [30] Lord H.W. and Shulman Y. (1967): A generalized dynamical theory of thermoelasticity. – J. Mech. Phys. Solids, vol.15, pp.299-309.
• [31] Luppe F., Conoir J.-M. and Norris A.N. (2012): Effective wave numbers for thermoviscoelastic media containing random configuration of spherical scatters. – J. Accoust. Soc. Am., vol.131, No.2, pp.1113-1120.
• [32] Mangin G.A. and Mild (1986): A solitary wave in micropolar elastic crystals. – Int. J. of Engineering Sciences, vol.24, pp.1474-1486.
• [33] Manole D. (1988): Theoreme d’unicite daus la theoris de la viscoelasticite linearic avec microstructure en utilisant la transformation de Laplace. – Rev. Roumania Sci. Tech. Ser. Mec. Appl., vol.33, pp.209-214.
• [34] Manole D. (1992): Variational theorem in linear theory of micropolar viscoelasticity. – But. Inst. Politehn. Lass; Sect., vol.38, pp.75-83.
• [35] McCharty M.F. and Eringen A.C. (1969): Micropolar viscoelasticity waves. – Int. J. Eng. Sci., vol.7, pp.447-458.
• [36] McKenzie J.K. (1950): The elastic constants of a solid containing spherical holes. – Proc. Phys. Soc. B6, pp.2-11.
• [37] Miglani A. and Kaushal S. (2011): Normal mode analysis of micropolar elastic medium with void under inviscid fluid. – Global Journal of Science Frontier Research, vol.11, No.4, pp.39-44.
• [38] Nowacki W. (1986): Theory of Asymmetric Elasticity. – Oxford: Pergamon Press.
• [39] Nunziato J.W. and Cowin S.C. (1979): A nonlinear theory of elastic materials with voids. – Arch. Rational Mech. Anal., vol.72, pp.175-201.
• [40] Puri P. and Cowin S.C. (1985): Plane waves in linear elastic materials with voids. – J. Elasticity, vol.15, pp.167-183.
• [41] Quintanilla R. (2001): On uniqueness and continuous dependence in the nonlinear theory of mixtures of elastic solids with voids. – Math Mech. Solids, vol.6, pp.281-298.
• [42] Scarpetta E. (1995): Wellposedness theorems for linear elastic materials with voids. – Int. J. Engng. Sci., vol.33, pp.151-161.
• [43] Singh J. and Tomar S.K. (2007): Plane waves in thermoelastic materials with voids. – Mechanics of Materials., vol.39, No.10, pp.932-940.
• [44] Svanadze M. (1988): The fundamental matrix of the linearized equations of the theory of elastic mixtures. – Proc. I. Vekua Inst. Appl. Math. Tbilisi State Univ., vol.23, pp.133-148.
• [45] Svandze M. (1996): The fundamental solution of the oscillation equations of thermoelasticity theory of mixtures of two solids. – Journal of Thermal Stresses, vol.19, pp.633-648.
• [46] Svandze M. (2004a): Fundamental solutions of the equations of the theory of thermoelasticity with microtemeratures. – Journal of Thermal Stresses, vol.27, pp.151-170.
• [47] Svandze M. (2004b): Fundamental solutions of the system of equations of steady osciallations in the theory of microstretch. – International Journal of Engineering Science, vol.42, pp.1897-1910.
• [48] Svandze M. (2007): Fundamental solutions in the theory of micropolar thermoelasticity for materials with voids. – Journal of Thermal Stresses, vol.30, pp.219-238.
• [49] Svandze M. (2012): Potential method in linear theories of viscoelasticity and thermoelasticity for Kelvin, Voigt materials. – Technische Mechanik, vol.32, No.2-5, pp.554-563.
• [50] Wright T.W. (1998): Elastic wave propagation through a material with voids. – J. Mech. Phys. Solids, vol.46, pp.2033-2047.