An analytical method for free vibration analysis of Timoshenko beam theory applied to cracked nanobeams using a nonlocal elasticity model

► The free vibration analysis of cracked nanobeams is investigated. ► This study is based on the theory of nonlocal elasticity and Timoshenko beam theory. ► The small scale effect parameter greatly affects the value of natural frequencies. ► Crack reduces the natural frequencies, causes a discontinuity in the cracked section.