The present problem deals with the thermo-elastic interaction of a gold nano-beam resonator induced by ramp-type heating under the two temperature theory of generalized thermoelasticity. The governing equations are constructed in the context of two-temperature three-phase-lag model (2T3P) and two-temperature Lord-Shulman (2TLS) model of generalized thermoelasticity. Using the Laplace transform, the fundamental equations have been expressed in the form of a vector-matrix differential equation which is then solved by Eigen value approach and Mathematica software package has been used as a tool. The inversion of Laplace transforms are computed numerically using the method of Fourier series expansion technique. Numerical results for lateral vibration, temperature, displacement, stress, and the strain energy are presented graphically for Lord-Shulman model and also for three-phase lag model. A numerical instance of gold nano-beam in femtoseconds scale has been calculated to present the effect of the ramping time parameter on the entire studied field. The effect of two-temperature parameter is also discussed on the physical fields.
This article deals with the thermoelastic interaction in a three-dimensional homogeneous and isotropic viscoelastic medium under the Dual-phase-lag model of generalized thermoelasticity. The resulting non-dimensional coupled equations are applied to a specific problem of a half-space whose surface is traction-free and is subjected to a time-dependent thermal shock. The analytical expressions for the displacement components, stress, temperature and strain are obtained in the physical domain by employing normal mode analysis. These expressions are also calculated for a copper-like material and have been depicted graphically. Discussions have been made to highlight the effect of viscosity on the studied field. The phenomenon of a finite speed of propagation is observed for each field. Also, if the effect of viscosity is neglected, the results agree with the existing literature.