Free vibration of cracked multi-span continuous functionally graded nanobeams

The free vibration of multiple cracked multi-span continuous functionally graded (FG) nanobeams is investigated based on Eringen’s nonlocal elastic theory (ENET). The massless three-spring model is employed to model transverse edged cracks. The governing equations for multiple cracked FG Euler–Bernoulli nanobeams are established by employing Hamilton’s principle, the ENET, and conditions of continuity at the crack locations. Analytical solutions are obtained to construct the dynamic stiffness matrix of nanobeam element. The proposed matrix enables an efficient and highly accurate free vibration analysis of cracked FG multi-span nanobeams while requiring only a minimal number of elements. The accuracy of the present approach is verified through numerical validations with previous works. The influences of nonlocal, material, and geometric parameters on the free vibration of multiple-cracked multi-span FG nanobeams are investigated in detail.