Transient thermoelastic response of a size‐dependent nanobeam under the fractional order thermoelasticity

Abstract

AbstractWith the miniaturization of structures, such as MEMS/NEMS, the size‐dependent effect has become an issue and attracted much attention. The well‐known theories describing the size‐dependent effect mainly include the nonlocal elasticity theory, the strain gradient theory and the modified coupled stress theory. Based on these theories, a number of works have been conducted to explore the size‐dependent behaviors of structures or devices in micro/nano‐scale, among them, majorities are on elastic performances, while, minorities are on thermoelastic performances. It is inevitable for structures suffering changeable temperature, as a consequence, thermal‐induced stress and deformation occur in structures and they are worth being fully concerned. For thermoelastic behaviors limited to small scale problems, the classical Fourier's heat conduction law may fail, meanwhile, new models, for example, fractional order heat conduction model, have been developed to modify Fourier's law. In present paper, the transient thermoelastic response of a nanobeam subjected to a ramp heating is investigated by combining the nonlocal elasticity theory and the fractional order heat conduction model. The governing equations are formulated and then solved by Laplace transform and its numerical inversion. The non‐dimensional temperature, displacement, stress, and deflection in the nanobeam are obtained and illustrated graphically. In calculation, the effects of the ramp‐heating time parameter, the nonlocal parameter and the fractional order parameter on the considered physical quantities are examined and discussed in detail.