Dynamic response of Timoshenko functionally graded beams with classical and non-classical boundary conditions using Chebyshev collocation method

This paper investigates the dynamic response of Timoshenko beams made of functionally graded materials (FGMs). The beams are supported by various classical and non-classical boundary conditions. By using Timoshenko beam theory to establish the governing equations of motion for describing the vibration behavior of the beams, the significant effects of shear deformation and rotary inertia are taken into account. Different mathematical models that is the power law, exponential and Mori–Tanaka models are used to describe material composition across the beam thickness. To predict accurate vibration behavior of the beams, the Chebyshev collocation method (CCM) is applied to solve the vibration problem of such beams. According to the numerical results, it is revealed that the proposed modeling and analysis method can provide accurate frequency results of the beams as compared to some cases in the literature. New frequency results of the beams with different material compositions and boundary conditions are also presented for future comparison and development.