Free vibration analysis of functionally graded Euler-Bernoulli and Timoshenko beams using Levy-type solution

In this paper, fundamental frequency of Functionally Graded (FG) beams with various boundary conditions is presented based on Classical Beam Theory (CBT) and First-order Beam Theory (FOBT). The material properties that vary across the thickness are determined by the power law. Governing equations of motion and boundary conditions are derived from the Hamilton’s principle. Levy-type solution is applied to analyse the effect of span-to-thickness ratio, power-law index and boundary conditions on the vibration behaviour of FG beams. Present results show that natural frequency decreases with an increase in power-law index and a decrease in span-to-thickness ratio. This work also corroborates the suggestion that the shear effect should be considered in studying natural vibration of FG moderate thick beams, especially for Clamped-Clamped or Clamped-Simply Support boundary conditions.