Generalized Coupled Thermo-elasticity of Beams Under a Lateral Thermal Shock

In this paper, the generalized themio-elastic response of a beam subjected to a uniform lateral thermal shock is analyzed. The beam is tnade of homogenous and isotropicmaterials and is assumed to follow the Hook s law for its constitutive behavior. The displacement field of the beam is approximated according to the first-order shear deformation theory. Also the linear strain-displacement relations are used for evaluating the strain field through the beam. The equations of motion of the beam, and theirassociated boundary conditions have all been extracted using Hamilton s principle. The Lord-Shulman (LS) energy equation has been employed for obtaining the temperature field through the beam. For solving the coupled governing equations, at first the temperature filed through the thickness of the beam is approximated by Legendre expansion. Then, the finite element and finite difference methods are used to discretization of the governing equations respectively in space and time domains. Results of the paper reveal the thermally induced vibrations of the beam under the applied thermal shock. Notably, results show the effects of the shear deformability and the thermo-mechanical coupling are considerable in comparison with the previous data in the literature.

کلیدواژه ها:

Shear deformable beam structures ، Coupled thermo—elasticity ، Lord-Shulman energy equation ، Lateral thennal shock ، Finite element method ، Finite difference method ، Legendre expansion