Small length scale coefficient for Eringen's and lattice-based continualized nonlocal circular arches in buckling and vibration

This paper presents analytical buckling and vibration solutions for two nonlocal circular arch models. One model is based on Eringen's stress gradient theory while the other model is based on continualization of a lattice system. Both nonlocal arch models contain the unknown small length scale coefficient e₀. In order to calibrate e₀, exact buckling and vibration solutions for Hencky bar-chain model (HBM) are first obtained. On the basis of the phenomenological similarities between the HBM and the nonlocal arch models, the matching of buckling and vibration solutions for HBMs and those for nonlocal models allows one to calibrate the e₀ values. It is found that e₀ for Eringen's nonlocal circular arch (ENCA) varies with respect to geometrical property of the arch and boundary conditions. However, e₀ for a continualized nonlocal circular arch (CNCA) is found to be a constant value, regardless of geometrical properties or boundary conditions.