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

•The dynamic analysis of multi-cracked gradient-elastic beams is presented.•Beam’s exact solutions under static point loads are used as Galerkin base functions.•The non-local model includes two length-scale parameters for strain and stress.•Beams with any number of cracks and any boundary conditions can be studied.•Microstructural effects increase with the modal wavelength over length-scale ratio. A 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 effects. 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 effort 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.