Elastic buckling and free vibration analysis of functionally graded Timoshenko beam with nonlocal strain gradient integral model

In this work, nonlocal strain gradient integral model is applied to study the elastic buckling and free vibration response of functionally graded (FG) Timoshenko beam which is made of two constituents varying along thickness direction. The differential governing equations and corresponding boundary conditions are derived via the Hamilton's principle, and the relations between nonlocal stresses and strains are expressed as integral equations. The...