Vibration Analysis of Bidirectional Functionally Graded Timoshenko Beams Using Chebyshev Collocation Method

This paper studies the vibration behaviors of bidirectional functionally graded (BDFG) Timoshenko beams based on the Chebyshev collocation method. The material properties of the beam are assumed to vary simultaneously in the beam length and thickness directions. The Chebyshev differentiation matrices are used to reduce the ordinary differential equations into a set of algebraic equations to form the eigenvalue problem for free vibration analysis. To validate the accuracy of the proposed model, some calculated results are compared with those obtained by other investigators. Good agreement has been achieved. Then the effects of slenderness ratios, material distribution types, gradient indexes, and restraint types on the natural frequency of BDFG beams are examined. Through the parametric study, the influences of the various geometric and material parameters on the vibration characteristics of BDFG beams are evaluated.