The vibration of thermoelastic silicon nitride Nanobeam based on green-naghdi theorem type-II subjected to mechanical damage and ramp-type heat

In this work, an analysis for thermoelastic homogeneous isotropic nanobeams under damage mechanics consideration was built. Under easily supported boundary conditions with fixed side ratios, the Green-Naghdi model type-II, an extended thermoelasticity theory model, has been utilized. For the governing differential equations, the Laplace transforms technique was used on the time variable. The answers were found in the domain of the Laplace transform. Tzou’s approximation approach based on an iteration formula was used to calculate the Laplace transform inversions numerically. The numerical findings for a rectangular silicon nitride thermoelastic nanobeam have been obtained and validated. As a case study, we assumed that the beam is thermally loaded with ramp-type heat and that its two edges are simply supported. Figures representing different scenarios have been used to display the numerical results. Mechanical damage value, ramp-time heat parameter and beam thickness are all reported to have a substantial influence on all of the examined functions.