The influence of the mechanical damage on a viscothermoelastic nanobeam due to ramp-type heating under Green-Naghdi theory type-II

The main object of this work is to analyze viscothermoelastic homogeneous and isotropic nanobeams under the effect of mechanical damage. A Green-Naghdi type-II model of thermoelasticity has been constructed under simply supported conditions. Moreover, the Laplace transforms have been applied for the governing differential equations. Tzou iteration method with approximation has been applied to calculate the Laplace inverse transforms. The numerical results are presented and validated for use in a viscothermoelastic rectangular nanobeam of silicon nitride when it has been thermally loaded by ramp-type heating and simple support. The numerical results have been demonstrated in different figures to stand on the effects of the mechanical damage variable, mechanical relaxation times parameters, and ramp-time heat parameter on all the studied functions. We conclude that the effect of the mechanical damage variable, ramp-time heating parameter, and mechanical relaxation times parameters are highly influential on all the studied functions and thermomechanical waves.