On the vibrations of a mechanically based non-local beam model

► Vibration analysis of a mechanically based non-local Timoshenko beam is pursued. ► Non-local effects result in long-range forces between non-adjacent volume elements. ► The motion equations are derived by applying the Hamilton's principle. ► The mechanical boundary conditions are not affected by non-local terms. ► Non-local effects on natural frequencies and vibrations modes are investigated.