Buckling and vibration of Hencky bar-chain with internal elastic springs

This paper presents the Hencky bar-chain model (HBM) that allows for the presence of internal elastic springs. With the development of this general HBM, one can analyse beam-like structures with repetitive cells with allowance for internal damaged sections or bracing members. In this paper, we have derived formulas for the internal rotational and lateral spring stiffnesses of HBMs based on the finite difference model (FDM). In addition, the analytical buckling loads and vibration frequencies of the HBM and FDM with internal elastic springs are presented for the first time. These analytical solutions converge to the exact solutions for continuum beams when the HBM segmental number approaches infinity. The solutions can also be used to calibrate the Eringen's small length scale coefficient e₀ in the nonlocal beam theory based on their phenomenological similarities.