Effects of different shear deformation theories on free vibration of functionally graded beams

• Free vibration of functionally graded (FG) beams is presented based on different shear deformation beam theories.
• Material properties of the beam vary along the thickness direction according to the power-law form.
• The origin in Cartesian coordinate system is taken at the center of FG beam.
• Trial functions denoting the displacement components are expressed in algebraic polynomial forms.
• Results in special cases are compared and new results are also incorporated.

Free vibration of functionally graded (FG) beams subjected to different sets of boundary conditions is examined in the present paper. Different higher-order shear deformation beam theories (SDBTs) have been incorporated for the free vibration response of FG beam. The material properties of FG beam are taken in the thickness direction in power-law form and trial functions denoting the displacement components are expressed in algebraic polynomials. The Rayleigh–Ritz method is used to estimate frequency parameters in order to handle to various sets of boundary conditions at the edges in a simple way. Comparison of frequency parameters is carried out with the existing literature in special cases and new results are also provided after checking the convergence of frequency parameters.