Perturbations for vibration of nano-beams of local/nonlocal mixture

Abstract. Here we extend the perturbation approach, previously presented in literature for Eringen’s two-phase local/nonlocal mixture model, to free vibration of purely flexible beams. In particular, expand eigenvalues and eigenvectors into power series fraction coefficient non-local material response up 2nd order. We show that family 0th order bending couples satisfy natural essential boundary conditions 1st order; hence, solution can conveniently be constructed using eigenspace with no necessity additional conditions. obtain condition solvability provides incremental eigenvalue closed form. further demonstrate increment is always negative, providing well-known softening effect long-range interactions among points a continuum modelled theory. examine simply supported beam as benchmark problem present