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Free transverse vibrational analysis of axially functionally graded tapered beams via the variational iteration approach

Tapered beams constitute functionally graded materials that are widely used in various engineering fields. The vibrational characteristics of tapered beams made of axially varying functionally graded materials are investigated via variational iteration method. Natural frequencies and corresponding mode shapes of axially functionally graded tapered beams are examined, and calculated frequencies are compared with results provided by previous researchers using other approximate methods. The efficiency and accuracy of this technique are demonstrated. The effect of nonhomogeneous material distribution, taper ratio as well as boundary conditions on the dynamical behavior of axially functionally graded tapered beams is thoroughly investigated as well.