Axisymmetric Free Vibrations of an Infinite Micropolar Thermoelastic Plate

Rajneesh Kumar; Geeta Partap

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Rajneesh Kumar, Geeta Partap. Axisymmetric Free Vibrations of an Infinite Micropolar Thermoelastic Plate[J]. Applied Mathematics and Mechanics, 2007, 28(3): 335-348.

Citation:

Rajneesh Kumar, Geeta Partap. Axisymmetric Free Vibrations of an Infinite Micropolar Thermoelastic Plate[J]. Applied Mathematics and Mechanics, 2007, 28(3): 335-348.

Citation:

Rajneesh Kumar, Geeta Partap. Axisymmetric Free Vibrations of an Infinite Micropolar Thermoelastic Plate[J]. Applied Mathematics and Mechanics, 2007, 28(3): 335-348.

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Axisymmetric Free Vibrations of an Infinite Micropolar Thermoelastic Plate

1.
Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India;

Received Date: 2006-03-07
Rev Recd Date: 2007-01-12
Publish Date: 2007-03-15

Abstract

Abstract

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated.The secular equations for homogeneous isotropic micropolar thermoe-lastic plate without energy dissipation in closed form for symmetric and skewsymmetric wave modes of propagation were derived.The different regions of secular equations were obtained.At short wave-length limits,the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation.The results for thermoelastic,micropolar elastic and elastic materials were obtained as particular cases from the derived secular equations.The amplitudes of displacement components,microrotation and temperature distribution were also computed during the symmetric and skew symmetric motion of the plate.The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components,microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes were presented graphically.The analytical and numerical results are found to be in close agreement.

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References(20)

References

[1]	Lord H W,Shulman Y A.A generalized dynamical theory of thermoelasticity[J].J Mech Phys Solids,1967,15(5):299-309. doi: 10.1016/0022-5096(67)90024-5
[2]	Green A E,Lindsay K L.Thermoelasticity[J].J Elasticity,1992, 2(1):1-7.
[3]	Green A E,Naghdi P M.A re-examination of the basic postulates of thermomechanics[J].Proceeding of the Royal Society London Ser A,1991,432(1885):171-194. doi: 10.1098/rspa.1991.0012
[4]	Green A E,Naghdi P M.On undamped heat waves in an elastic solid[J].Journal of Thermal Stresses,1992,15(2):253-264. doi: 10.1080/01495739208946136
[5]	Green A E,Naghdi P M.Thermoelasticity without energy dissipation[J].J Elasticity,1993,31(3):189-208. doi: 10.1007/BF00044969
[6]	Green A E,Naghdi P M.A unified procedure for construction of theories of deformable media Ⅰ.Classical continuum physics Ⅱ. Generalized continua Ⅲ, Mixtures of interacting continua[J].Proceeding of the Royal Society London Ser A,1995,448(1934): 335-356,357-377,379-388. doi: 10.1098/rspa.1995.0020
[7]	Chandrasekharaiah D S.A uniqueness theorem in the theory of thermoelasticity without energy dissipation[J].Journal of Thermal Stresses,1966,19(3):267-272.
[8]	Chandrasekharaiah D S.A note on uniqueness of solution in the linear theory of thermoelasticity without energy dissipation[J].J Elasticity,1996,43(3):279-283. doi: 10.1007/BF00042504
[9]	Scott N H.Energy and dissipation of inhomogeneous plane waves in thermoelasticity[J].Wave Motion,1996,23(4):393-406. doi: 10.1016/0165-2125(96)00003-0
[10]	Chandrasekharaiah D S,Srinath K S.Axisymmetric thermoelastic interaction without energy dissipation in an unbounded body with cylindrical cavity[J].J Elasticity,1997,46(1):19-31. doi: 10.1023/A:1007333502283
[11]	Chandrasekharaiah D S,Srinath K S.Thermoelastic waves without energy dissipation in an unbounded body with spherical cavity[J].Int J Math Math Sci,2000,23(8):555-562. doi: 10.1155/S0161171200001514
[12]	Iesan D.On the theory of thermoelasticity without energy dissipation[J].Journal of Thermal Stresses,1998,21(3):295-307. doi: 10.1080/01495739808956148
[13]	Quintanilla R.On the spatial behavior in Thermoelasticity without energy dissipation[J].Journal of Thermal Stresses,1999,22(2):213-224. doi: 10.1080/014957399280977
[14]	Wang J,Slattery S P.Thermoelasticity without energy dissipation for initially stressed bodies[J].Int J Math Math Sci,2002,31(6):329-337. doi: 10.1155/S0161171202105023
[15]	Quintanilla R.Thermoelasticity without energy dissipation of nonsimple materials[J].Journal of Appl Math Mech (ZAMM),2003,83(3):172-180.
[16]	Kumar R,Deswal S.Surface wave propagation through a cylindrical bore in a micropolar generalized thermoelastic medium without energy dissipation[J].Proc Nat Acad Sci,2003,73(A)(3):315-327.
[17]	Kumar R,Deswal S.Surface wave propagation in a micropolar thermoelastic medium without energy dissipation[J].J Sound and Vibration,2002,256(1):173-178. doi: 10.1006/jsvi.2001.4175
[18]	Eringen A C.Linear theory of micropolar elasticity[J].J Math Mech,1966,15(6):909-923.
[19]	Lamb H.On waves in an elastic plate[J].Phil Trans Roy Soc,London, Ser A,1917,93:114-128.
[20]	Graff K F.Wave Motion in Elastic Solids[M].New York:Dover publications Inc,1991.