Abstract
The present article focuses on the new meticulous model based on the postulate of memory-dependent derivatives to analyze the thermo-mechanical interactions inside the nano-beam-based machined resonators. Also, the size effect on dynamic responses of thermoelastic vibrations of homogeneous and isotropic nano-beam is considered. The fundamental expressions are formulated in the frame of non-local generalized thermoelasticity with paired relaxation times by operating the results of Euler-Bernoulli beam theory, non-local effect, and memory-dependent derivative. The proposed model is applied to study the nano-beam-based machined resonator subjected to the ramp-type heating and exponentially decaying time-dependent load. Closed-form solutions of the physical fields are examined by applying the Laplace transform mathematical mechanism. However, the coherence of the new thermal conductivity framework, a collation has been bestowed among the results obtained in the presence or absence of the memory-dependent derivative; also, the size effect is analyzed on the significant parameters of nano-beam such as deflection, temperature, displacement as well as bending moment. Moreover, the prominent influence of the distinct affecting parameters such as constituents of memory-dependent derivative (kernel function and time delay) and ramping time parameter with an applied load on the physical fields have been investigated with the help of quantitative results.