Develop a refined truncated cubic lattice structure for nonlinear large-amplitude vibrations of micro/nano-beams made of nanoporous materials

Pore size and interconnectivity have essential role in different biological applications of synthetic porous biomaterials. Recent improvements in technology make it possible to produce nanoporous materials having pores of controllable dimensions at atomic scale. In the present study, based upon a refined truncated cube lattice structure, the elastic mechanical properties of nanoporous materials have been extracted explicitly in terms of the pore size. Afterwards, the size-dependent nonlinear large-amplitude vibrations of micro/nano-beams made of the nanoporous material are explored. To this purpose, the nonlocal strain gradient elasticity theory is utilized within the framework of the refined hyperbolic shear deformation beam theory to capture the both small-scale effects of hardening-stiffness and softening-stiffness. Finally, the Galerkin method together with an improved perturbation technique is employed to construct explicit analytical expression for the nonlocal strain gradient frequency-deflection response of micro/nano-beams made of nanoporous materials. It is demonstrated that, by increasing the pore size, the nonlinear frequency associated with the large-amplitude vibration of micro/nano-beams made of nanoporous material reduces, but the rate of this reduction becomes lower for higher pore size.