We consider a 2D problem of a circular cylinder that is infinitely long and whose external surface is free from outside effects and acted upon by an asymmetrical temperature distribution that is harmonic in time. The problem is within the context of the theory of thermoelasticity without energy dissipation. The exact solution is obtained by a direct approach. The results are represented graphically and discussed.
BiotMA.Thermoelasticity and irreversible thermodynamics. J Appl Phys1956; 27: 240–253.
2.
LordHShulmanY.A generalized dynamical theory of thermoelasticity. J Mech Phys Solids1967; 15: 299–309.
3.
DhaliwalRSheriefH.Generalized thermoelasticity for anisotropic media. Quart Appl Math1980; 33: 1–8.
4.
SheriefHHamzaFSalehH.The theory of generalized thermoelastic diffusion. Int J Eng Sci2004; 42: 591–608.
5.
SheriefHHamzaFEl-SayedA.Theory of generalized micropolar thermoelasticity and an axisymmetric half-space problem. J Therm Stresses2005; 28: 409–437.
6.
SheriefHAllamMElhagaryM.Generalized theory of thermoviscoelasticity and a half-space problem. Int J Thermophys2011; 32: 1271–1295.
7.
SheriefHHusseinE.A mathematical model for short-time filtration in poroelastic media with thermal relaxation and two temperatures. Transp Porous Med2012; 91: 199–223.
8.
SheriefHEl-SayedAAbd El-LatiefA.Fractional order theory of thermoelasticity. Int J Solids Struct2010; 47: 269–275.
9.
SheriefHElhagaryM.Fractional order theory of thermo-viscoelasticity and application. Mech Time-Depend Mater2020; 24: 179–195.
10.
SheriefHAnwarM.A problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials. J Therm Stresses1989; 12: 529–543.
11.
SheriefHElmisieryAElhagaryM.Generalized thermoelastic problem for an infinitely long hollow cylinder for short times. J Therm Stresses2004; 27: 885–902.
12.
ElhagaryM.A two-dimensional problem for two media in the generalized theory of thermoelasticity. J Therm Stresses2010; 33: 1–15.
13.
SheriefHEl-MaghrabyNAllamA.Stochastic thermal shock problem in generalized thermoelasticity. Appl Math Model2013; 37: 762–775.
14.
ElhagaryM.A two-dimensional generalized thermoelastic diffusion problem for a thick plate subjected to thermal loading due to laser pulse. J Therm Stresses2014; 37: 1416–1432.
GreenANaghdiP.Thermoelasticity without energy dissipation. J Elasticity1993; 31: 189–208.
17.
ChandrasekharaiahD.A uniqueness theorem in the theory of thermoelasticity without energy dissipation. J Thermal Stresses1996; 19: 267–272.
18.
ChandrasekharaiahD.One-dimensional wave propagation in the linear theory of thermoelasticity without energy dissipation. J Thermal Stresses1996; 19: 695–710.
19.
ChandrasekharaiahDSrinathK.Thermoelastic interactions without energy dissipation due to a point heat source. J Elasticity1998; 50: 97–108.
20.
KimJBaiKErtekinRWebsterW.A derivation of the Green-Naghdi equations for irrotational flows. J Eng Math1002; 40: 17–42.
21.
QuintanillaR.Existence in thermoelasticity without energy dissipation. J Thermal Stresses2002; 25: 195–202.
22.
RoychoudhuriSDuttaPS.Thermo-elastic interaction without energy dissipation in an innite solid with distributed periodically varying heat sources. Int J Solids Struct2005; 42: 4192–4203.
23.
SharmaJN.On the problems of body forces and heat sources in thermoelasticity without energy dissipation. Indian J Pure Appl Math1999; 30: 595–610.
24.
MukhopadhyayS.Thermoelastic interactions without energy dissipation in an unbounded body with a spherical cavity subjected to harmonically varying temperature. Mech Res Commun2004; 31: 81–89.
25.
MukhopadhyayS.Thermoelastic interactions without energy dissipation in an unbounded medium with a spherical cavity due to a thermal shock at the boundary. J Thermal Stresses2002; 25: 877–887.
26.
Abd El-LatiefAMKhaderSE.Exact solution of thermoelastic problem for a one-dimensional bar without energy dissipation. ISRN Mech Eng2014; 1–6.
27.
SheriefHHRaslanWE.A 2D problem of thermoelasticity without energy dissipation for a sphere subjected to axisymmetric temperature distribution. J Thermal Stresses2017; 40: 1461–1470.
28.
SpiegelM.Mathematical handbook. New York: McGraw-Hill, 1996.
