Free vibration analysis of thin and thick-walled FGM box beams

Free vibration of FGM box beam is investigated by the formulation of an exact dynamic stiffness matrix on the basis of first-order shear deformation theory (FSDT). Primary and secondary torsional warping, shear and bending deformations are incorporated in the one-dimensional beam model. Material properties of the beam are assumed to be graded across the wall-thickness. A recent function characterising the distribution of shear stresses is introduced. The present model is validated by comparison with finite element analysis for various boundary conditions. Good correlation exists between the values of Abaqus analysis and those calculated with the present method.

► This is the first study on free vibrations of thin and thick-walled FGM box beams.
► Primary and secondary torsional warping is considered.
► The governing equations are found by applying Hamilton's principle.
► Newton's eigenvalue iteration method was used to obtain frequencies.