Free and Forced Vibration Analysis of Composite Beam Composed Laminated Composite Material and Functionally Graded Material

This paper presents the dynamic characteristic analysis of a multi-layer composite beam (MLCB) composed of a laminated composite beam (LCB) and functionally graded beam (FGB) for the first time.

MLCB has new material properties because the fiber-reinforced material is laminated in the middle layer in the z direction, and the FGB are laminated above and below it. Theoretical formulations are established based on the first-order share deformation beam theory (FSDBT) and the solution results, such as the natural frequency of the beam, are obtained by applying the Rayleigh–Ritz method. With the introduction of the artificial spring technique, the boundary conditions of the MLCB are modeled as arbitrary boundary conditions, including classical boundary conditions and elastic boundary conditions. All displacement functions are represented by four different polynomials such as the Chebyshev, Legendre and the orthogonal polynomials.

The vibration results of MLCBs with new material properties obtained using this method are verified for accuracy and convergence by comparing them with published literature and FEM results. The new vibration characteristics results of the MLCB with different lamination scheme, boundary conditions and geometric dimensions are given through numerical examples. These new numerical results can be used as benchmark data for research in this field.