Eigenvalue approach to nanobeam in modified couple stress thermoelastic with three-phase-lag model induced by ramp type heating

This article deals with the study of a thermoelastic nanobeam in a modified couple stress
theory subjected to ramp-type heating. The mathematical model is prepared for the nanobeam
in thermoelastic three-phase-lag. The Laplace transform and the eigenvalue approach are
used to find the displacement component, lateral deflection, temperature change and axial
stress of the thermoelastic beam. The general algorithm of the inverse Laplace transform is
developed to compute results numerically. The comparison of three-phase-lag, dual-phaselag
and GN-III (1993) models are represented, and their illustration is depicted graphically.
This study finds the applications in engineering, medical science, sensors, etc.