Functionally graded materials (FGMs) have wide applications in different branches of engineering such as aerospace, mechanics, and biomechanics. Investigation of the mechanical behaviors of structures made of these materials has been performed widely using classical elasticity theories in micro/nano scale. In this research, static, dynamic and vibrational behaviors of functional micro and nanobeams were investigated using non-local theory. Governing linear equations of the problem were driven using non-local theory and solved using an analytical method for different boundary conditions. Effects of the axial load, the non-local parameter and the power index on the natural frequency of different boundary condition are assessed. Then, the obtained results were compared with those obtained from classical theory. These results showed that a non-local effect could greatly affect the behaviors of these beams, especially at nano scale.
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