Thermoelastic vibrations of nano-beam with varying axial load and ramp type heating under the purview of Moore-Gibson-Thompson generalized theory of thermoelasticity

Development in nanotechnology is found to be the first choice for the researchers nowadays due to its specific property to deal with the manufacturing of materials and structures at nanoscale level. The study of mechanical as well as thermal behaviour of nano-beams is a vital part of the branch of nanostructure due to its promising applications in designing the micro-nano-electro-mechanical systems in precise manner. The present contribution enlightens the analysis of thermoelastic vibrations of a nano-beam subjected to a variable axial load. Both ends of the beam are considered to be clamped. In contrast to the previous studies where the initial axial load is assumed to be constant, the present study deals with the axial load depending on time. Mathematical modelling of the beam is performed by considering the concept of Euler-Bernoulli beam theory. A new generalized thermoelastic model known as Moore-Gibson generalized thermoelastic (MGTE) model is addressed to study the thermal effects inside the beam. The analytical outcomes to the physical fields such as lateral vibration (deflection), temperature, displacement, bending moment as well as thermal stress are evaluated by adopting the mechanism of the Laplace transform technique. The quantitative results are established in time domain for each physical field by taking the numerical inversion of Laplace transform. In order to execute the attractiveness of MGTE model, the quantitative results are compared to the other thermoelastic models such as classical thermoelastic (CTE) model, Lord-Shulman (LS) model, Green-Naghdi-II, III (GN-II, GN-III) models. Significant influence of the thermoelastic models, axial load as well as ramping time parameter is investigated on nano-beam response and represented graphically.