The vibration of a viscothermoelastic nanobeam of silicon nitride with variable thermal conductivity induced by ramp-type thermal loading

In the present paper, the analysis has been constructed for thermoelastic homogeneous isotropic nanobeams. A generalized model of the viscothermoelasticity theory of one relaxation time with variable thermal conductivity has been used under simply supported conditions for fixed aspect ratios. Laplace transform has been applied for the governing differential equations. The inverse of the Laplace transform has been calculated by using the Tzou approximation method. The numerical results have been validated for a thermoelastic rectangular nanobeam of silicon nitride as a case when it is subjected to ramp-type heating and simply supported. The numerical results have been shown in figures to stand on the viscothermoelastic parameter's effects and the ramp-type heat parameter. The effect of the variability of thermal conductivity is a very significant consideration. The nanobeam thickness has a significant impact on all the studied state functions.