Characterization of the Vibration and Strain Energy Density of a Nanobeam under Two-Temperature Generalized Thermoelasticity with Fractional-Order Strain Theory

In this work, fractional-order strain theory was applied to construct a novel model that introduces a thermal analysis of a thermoelastic, isotropic, and homogeneous nanobeam. Under supported conditions of fixed aspect ratios, a two-temperature generalized thermoelasticity theory based on one relaxation time was used. The governing differential equations were solved using the Laplace transform, and their inversions were found by applying the Tzou technique. The numerical solutions and results for a thermoelastic rectangular silicon nitride nanobeam were validated and supported in the case of ramp-type heating. Graphs were used to present the numerical results. The two-temperature model parameter, beam size, ramp-type heat, and beam thickness all have a substantial influence on all of the investigated functions. Moreover, the parameter of the ramp-type heat might be beneficial for controlling the damping of nanobeam energy.

Diagonalization Method to Hyperbolic Two-Temperature Generalized Thermoelastic Solid Sphere under Mechanical Damage Effect

This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.

Initial Stress and Gravity on P-Wave Reflection from Electromagneto-Thermo-Microstretch Medium in the Context of Three-Phase Lag Model

The present paper studied the reflection of thermo-microstretch waves under the generalized thermoelasticity theory which is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of the electromagnetic field, initial stress, and gravity. The formulation is applied under the thermoelasticity theory with three-phase lag, and the reflection coefficient ratio variations with the angle of incidence under different conditions are obtained. Numerical results obtained from the present study are presented graphically and discussed. It is observed that the initial stress, gravitation, and electromagnetic field exert some influence in the thermo-microstretch medium due to reflection of P-waves.