Dynamic analysis of multi-cracked Euler-Bernoulli beams with gradient elasticity

Galerkin-type approach is presented and numerically validated for the vibration analysis of non-local slender beams with multiple cracks, in which a hybrid gradient elasticity (HGE) model accounts for the microstructural e ects. It is shown that: i) a smoother and more realistic profile of beam’s rotations is obtained at the damaged locations; ii) independently of support restraints and damage scenarios, only four boundary conditions are required, meaning that the computational e ort does not increase with the number of cracks; iii) the microstructural effects become significant when the modal wave lengths are less then about forty times the HGE length-scale parameters.