A modeling method for vibration analysis of cracked laminated composite beam of uniform rectangular cross-section with arbitrary boundary condition

This paper establishes an analysis model to study the vibration behavior of a cracked laminated composite beam with uniform rectangular cross-section based on the Jacobi-Ritz method and the first-order shear deformation theory (FSDT). The boundary conditions of both ends of the cracked laminated beam are modeled as the elastic spring and the beam is divided into two parts by the crack section. The continuous conditions at the connecting face are modeled by the inverse of the flexibility coefficients of the fracture mechanics theory. Ignoring the influence of boundary conditions, displacements admissible functions of cracked laminated beam can be set up as Jacobi orthogonal polynomials. The accuracy and robustness of the present method are evidenced through comparison with previous literature and the results achieved by the finite element method (FEM). Numerical examples are given for free vibration analysis of cracked laminated composite beams with various boundary conditions, which may be provided as reference data for future study.