An analytical method for free vibration analysis of functionally graded beams

A new beam theory different from the traditional first-order shear deformation beam theory is used to analyze free vibration of functionally graded beams. The beam properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. It is assumed that the lateral normal stress of the beam is zero and the governing equations of motion are derived using Hamilton’s principle. Resulting system of ordinary differential equations of free vibration analysis is solved using an analytical method. Different boundary conditions are considered and comparisons are made among different beam theories. Also, the effects of boundary conditions, volume fraction and shear deformation on natural frequencies and mode shapes are investigated.