Numerical analysis of the damage mechanics variable and vibration of a viscothermoelastic microbeam with variable thermal conductivity

Abstract

In the present paper, the analysis for thermoelastic homogeneous isotropic microbeams has been constructed. A generalized viscothermoelasticity theory of one relaxation time with variable thermal conductivity in the context of damage mechanics definition has been applied based on simply supported conditions for aspect ratios. Laplace transform has been applied for the governing differential equations, and its inverse has been carried out by using the Tzou method. Microbeam of silicon nitride has been considered when it is subjected to ramp-type heating and simply supported. The results have been illustrated in figures to stand on the impacts of the viscothermoelastic parameter, the thermal conductivity parameter, the value of the beam thickness, and the ramp-type heating parameter. The influences of the mentioned parameters are significant on all the studied functions, and the ramp-type heating parameter plays a vital role in thermodynamically damping of the energy which has been generated on the beam.

The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

“…The current figures agree with the figures in the Youssef et al 43 especially, the temperature increment and stress distributions which guarantee the validity of the current results.…”