A temperature-dependent vibration analysis is studied for functionally graded nanocomposite beams reinforced by graphene. Material properties are assumed to change along the beam in five different types according to the graphene distribution with a specific function. The differential equations of motion are extracted and solved by spectral numerical method for the beam under various boundary conditions. The effect of distribution of functionally graded nanocomposite in the thickness direction of beam on frequency response of vibration and the effect of various parameters such as distribution function of nanographene plates, weight percentage, dimensions of nanographene plates, temperature changes, and thickness ratio on vibration response has been examined. The results are compared and validated with numerical and analytical results reported in references for manifold boundary conditions. It is seen that the increase of graphene weight percentage in all boundary conditions will increase natural frequency in the beam.
