In this manuscript the dynamic response of porous functionally-graded (FG) Bernoulli-Euler nano-beams subjected to hygro-thermal environments is investigated by the local/nonlocal stress gradient theory of elasticity. In particular, the influence of several parameters on both the thermo-elastic material properties and the structural response of the FG nano-beams, such as material gradient index, porosity volume fraction, nonlocal parameter, gradient length parameter, and mixture parameter is examined. It is shown how the proposed approach is able to capture the dynamic behavior of porous functionally graded Bernoulli-Euler nano-beams under hygro-thermal loads and leads to well-posed structural problems of nano-mechanics.
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